Scriabin was born in Moscow into a Russian noble family on Christmas Day 1871 according to the Julian Calendar. His father Nikolai Aleksandrovich Scriabin (1849–1915), then a student at the Moscow State University, belonged to a modest noble family founded by Scriabin's great-grandfather Ivan Alekseevich Scriabin, a simple soldier from Tula who made a brilliant military career and was granted hereditary nobility in 1819. Alexander's paternal grandmother Elizaveta Ivanovna Podchertkova, daughter of a captain lieutenant Ivan Vasilievcih Podchertkov, came from a wealthy noble house of the Novgorod Governorate. His mother Lyubov Petrovna Scriabina (née Schetinina) (1850–1873) was a concert Pianist and a former student of Theodor Leschetizky. She belonged to the ancient dynasty that traced its history back to Rurik; its founder, Semyon Feodorovich Yaroslavskiy nicknamed Schetina (from the Russian schetina meaning stubble), was the great-grandson of Vasili, Prince of Yaroslavl. She died of tuberculosis when Alexander was only a year old.

In 1882 he enlisted in the Second Moscow Cadet Corps. As a student, he became friends with the actor Leonid Limontov, although in his memoirs Limontov recalls his reluctance to become friends with Scriabin, who was the smallest and weakest among all the boys and was sometimes teased due to his stature. However, Scriabin won his peers' approval at a concert where he performed on the piano. He ranked generally first in his class academically, but was exempt from drilling due to his physique and was given time each day to practise at the piano.

In 1892 he graduated with the Little Gold Medal in piano performance, but did not complete a composition degree because of strong differences in personality and musical opinion with Arensky (whose faculty signature is the only one absent from Scriabin's graduation certificate) and an unwillingness to compose pieces in forms that did not interest him.

In 1894 Scriabin made his debut as a Pianist in St. Petersburg, performing his own works to positive reviews. During the same year, Mitrofan Belyayev agreed to pay Scriabin to compose for his publishing company (he published works by notable composers such as Nikolai Rimsky-Korsakov and Alexander Glazunov). In August 1897, Scriabin married the young Pianist Vera Ivanovna Isakovich, and then toured in Russia and abroad, culminating in a successful 1898 concert in Paris. That year he became a Teacher at the Moscow Conservatory, and began to establish his reputation as a Composer. During this period he composed his cycle of études, Op. 8, several sets of preludes, his first three piano sonatas, and his only piano concerto, among other works, mostly for piano.

While Scriabin wrote only a small number of orchestral works, they are among his most famous, and some are performed frequently. They include a piano concerto (1896), and five symphonic works, including three numbered symphonies as well as The Poem of Ecstasy (1908) and Prometheus: The Poem of Fire (1910), which includes a part for a machine known as a "clavier à lumières", known also as a Luce (Italian for "Light"), which was a colour organ designed specifically for the performance of Scriabin's tone poem. It was played like a piano, but projected coloured light on a screen in the concert hall rather than sound. Most performances of the piece (including the premiere) have not included this light element, although a performance in New York City in 1915 projected colours onto a screen. It has been claimed erroneously that this performance used the colour-organ invented by English Painter A. Wallace Rimington when in fact it was a novel construction supervised personally and built in New York specifically for the performance by Preston S. Miller, the President of the Illuminating Engineering Society.

According to later reports, between 1901 and 1903 Scriabin envisioned writing an opera. He talked a lot about it and expounded its ideas in the course of normal conversation. The work would center around a Nameless hero, a philosopher-musician-poet. Among other things, he would declare: I am the apotheosis of world creation. I am the aim of aims, the end of ends. The Poem Op. 32 No. 2 and the Poème Tragique Op. 34 were originally conceived as arias in the opera.

The development of Scriabin's style can be traced in his ten piano sonatas: the earliest are composed in a fairly conventional late-Romantic manner and reveal the influence of Chopin and sometimes Franz Liszt, but the later ones are very different, the last five being written without a key signature. Many passages in them can be said to be atonal, though from 1903 through 1908, "tonal unity was almost imperceptibly replaced by harmonic unity."

By the winter of 1904, Scriabin and his wife had relocated to Switzerland, where he began work on the composition of his Symphony No. 3. While living in Switzerland, Scriabin was separated legally from his wife, with whom he had had four children. The work was performed in Paris during 1905, where Scriabin was now accompanied by Tatiana Fyodorovna Schloezer—a former pupil and the niece of Paul de Schlözer. With Schloezer, he had other children, including a son named Julian Scriabin, a precocious Composer of several piano works before he drowned in the Dnieper River at Kiev in 1919 at the age of 11.

Scriabin's second wife Tatiana Fyodorovna Schlözer was the niece of the Pianist and possible Composer Paul de Schlözer. Her brother was the music critic Boris de Schlözer. Scriabin had seven children in total: from his first marriage Rimma (Rima), Elena, Maria and Lev, and from his second Ariadna, Julian and Marina. Rimma died of intestinal issues in 1905 at the age of seven. Elena Scriabina was to become the first wife of the Pianist Vladimir Sofronitsky, though only after her father's death; hence Sofronitsky never met the Composer. Maria Skryabina (1901–1989) became an Actress at the Second Moscow Art Theatre and the wife of Director Vladimir Tatarinov. Lev also died at the age of seven, in 1910. At this point, relations with Scriabin's first wife had significantly deteriorated, and Scriabin did not meet her at the funeral.

Scriabin's daughter Ariadna Scriabina (1906–1944) became a hero of the French Resistance, and was posthumously awarded the Croix de guerre and the Médaille de la Résistance. Her third marriage was to the poet and WWII Resistance fighter David Knut after which she converted to Judaism and took the name Sarah. She co-founded the Zionist resistance movement Armée Juive and was responsible for communications between the command in Toulouse and the partisan forces in the Tarn district and for taking weapons to the partisans, which resulted in her death when she was ambushed by the French Militia.

In 1907, he settled in Paris with his family and was involved with a series of concerts organized by the impresario Sergei Diaghilev, who was actively promoting Russian music in the West at the time. He relocated subsequently to Brussels (rue de la Réforme 45) with his family.

Scriabin was interested in Friedrich Nietzsche's Übermensch theory, and later became interested in Theosophy. Both would influence his music and musical thought. During 1909–10 he lived in Brussels, becoming interested in Jean Delville's Theosophist philosophy and continuing his reading of Helena Blavatsky.

Scriabin himself made recordings of 19 of his own works, using 20 piano rolls, six for the Welte-Mignon, and 14 for Ludwig Hupfeld of Leipzig. The Welte rolls were recorded during early February 1910, in Moscow, and have been replayed and published on CD. Those recorded for Hupfeld include the piano sonatas Op. 19 and 23. While this indirect evidence of Scriabin's pianism prompted a mixed critical reception, close analysis of the recordings within the context of the limitations of the particular piano roll Technology can shed light on the free style that he favoured for the performance of his own works, characterized by extemporary variations in tempo, rhythm, articulation, dynamics, and sometimes even the notes themselves.

Scriabin's funeral, on 16 April 1915, was attended by such numbers that tickets had to be issued. Rachmaninoff, who was a pallbearer at the funeral, subsequently went on tour, playing only Scriabin's music, for the benefit of the family. Sergei Prokofiev admired the Composer, and his Visions Fugitives bears great likeness to Scriabin's tone and style. Another admirer was the English Composer Kaikhosru Sorabji, who promoted Scriabin even during the years when his popularity had decreased greatly. Aaron Copland praised Scriabin's thematic material as "truly individual, truly inspired", but criticized Scriabin for putting "this really new body of feeling into the strait-jacket of the old classical sonata-form, recapitulation and all", calling this "one of the most extraordinary mistakes in all music."

Scriabin's music was greatly disparaged in the West during the 1930s. Sir Adrian Boult refused to play the Scriabin selections chosen by the BBC programmer Edward Clark, calling it "evil music", and even issued a ban on Scriabin's music from broadcasts in the 1930s. In 1935, Gerald Abraham described Scriabin as a "sad pathological case, erotic and egotistic to the point of mania". Scriabin has since undergone a total rehabilitation.

In total, three of Ariadna Scriabina's children immigrated to Israel after the war, where her son Eli (born 1935) became a Sailor in the Israeli Navy and a noted classical Guitarist, while her son Joseph (Yossi) (born 1943) served in the Israeli special forces, before becoming a poet, publishing many poems dedicated to his mother Ariadna. One of her great-grandsons, via Betty (Elizabeth) Lazarus, Elisha Abas, is an Israeli concert Pianist.

Ariadna Scriabina's daughter (by her first marriage to French Composer David Lazarus), Betty Knut-Lazarus, became a famous teenage heroine of the French Resistance, personally winning the Silver Star from George S. Patton, as well as the French Croix de guerre. After the war she became an active member of the Zionist Lehi (Stern Gang), undertaking special operations for the militant group and she was imprisoned in 1947 for launching a terrorist letter bomb campaign against British targets, and planting explosives on British ships which had been trying to prevent Jewish immigrants from travelling to Mandatory Palestine. Regarded as a heroine in France, she was released prematurely, but was imprisoned a year later in Israel for being allegedly involved in the killing of Folke Bernadotte, but the charges were subsequently dropped. After her release from prison, she settled at the age of 23 in Beersheba in Southern Israel, where she had three children and she founded a nightclub which became the cultural centre of Beersheba, before her early death at the age of 38.

Scriabin was the uncle of Metropolitan Anthony Bloom of Sourozh, a renowned bishop in the Russian Orthodox Church who directed the Russian Orthodox diocese in Great Britain between 1957 and 2003. Scriabin was not a relative of Soviet Minister of Foreign Affairs Vyacheslav Molotov, whose birth name was Vyacheslav Skryabin. In his memoirs published by Felix Chuyev under the Russian title "Молотов, Полудержавный властелин", Molotov explains that his brother Nikolay Skryabin, who was also a Composer, had adopted the name Nikolay Nolinsky in order not to be confused with Alexander Scriabin.

On November 22, 1969, the work was fully realized making use of the composer’s color score as well as newly developed laser Technology on loan from Yale’s Physics Department, by John Mauceri and the Yale Symphony Orchestra and designed by Richard N. Gould, who projected the colors into the auditorium that were reflected by the Mylar vests worn by the audience. The Yale Symphony repeated the presentation in 1971 and brought the work to Paris that year for what was perhaps its Paris premiere at the Théâtre des Champs Élysées. The piece was reprised at Yale once again in 2010 (as conceived by Anna M. Gawboy on YouTube, who, with Justin Townsend, has published ‘Scriabin and the Possible’).

In 2009 Roger Scruton described Scriabin as "one of the greatest of modern composers".

Scriabin's early harmonic language was specially fond of the thirteenth dominant chord, usually with the 7th, 3rd, and 13th spelled in fourths. This voicing can also be seen in several of Chopin's works. According to Peter Sabbagh, this voicing would be the main generating source of the later Mystic chord. More importantly, Scriabin was fond of simultaneously combining two or more of the different dominant seventh enhancings, like 9ths, altered 5ths, and raised 11ths. However, despite these tendencies, slightly more dissonant than usual for the time, all these dominant chords were treated according to the traditional rules: the added tones resolved to the corresponding adjacent notes, and the whole chord was treated as a dominant, fitting inside tonality and diatonic, functional harmony.

In 2015, German-Australian Pianist Stefan Ammer, as a part of The Scriabin Project Concert Series, joined forces alongside his pupils Mekhla Kumar, Konstantin Shamray and Ashley Hribar to honour the Russian Composer at various venues across Australia.