Edgar Froese arrived in West Berlin in the mid-1960s to study art. His first band, the psychedelic rock-styled The Ones, disbanded after releasing only one single. After The Ones, Froese experimented with musical ideas, playing smaller gigs with a variety of Musicians. Most of these performances were in the famous Zodiak Free Arts Lab, although one grouping also had the distinction of being invited to play for the surrealist Painter Salvador Dalí. The music was partnered with literature, painting, early forms of multimedia, and more. It seemed as though only the most outlandish ideas attracted any attention, leading Froese to comment, "In the absurd often lies what is artistically possible." As members of the group came and went, the direction of the music continued to be inspired by the Surrealists, and the group came to be called by the surreal-sounding name of Tangerine Dream, inspired by the line "tangerine trees and marmalade skies" from The Beatles' track "Lucy in the Sky with Diamonds."

Through the 1970s and 1980s the band toured extensively. The concerts generally included large amounts of unreleased and improvised material, and were consequently widely bootlegged. They were notorious for playing extremely loudly (reaching 134 dB in 1976) and for a long time. The band released recordings of a fair number of their concerts, and on some of these the band worked out material which would later form the backbone of their studio recordings (for Example, Pergamon, which documents a concert given in East Berlin shortly after Johannes Schmoelling joined the group, contains themes that would appear later on Tangram). An early Example of this was the Ricochet album, which was recorded during a tour that included European cathedrals, with some later overdubbing.

A number of other members were also part of Tangerine Dream for shorter periods of time. Unlike session Musicians, these players also contributed to compositions of the band during their tenures. Some of the more notable members are Steve Schroyder (organist, 1971–72), Michael Hoenig (who replaced Baumann for a 1975 Australian tour and a London concert, included on Bootleg Box Set Vol. 1), Steve Jolliffe (wind instruments, keyboards and vocals on Cyclone and the following tour; he was also part of a short-lived 1969 line-up), Klaus Krieger (drummer on Cyclone and Force Majeure) and Ralf Wadephul (in collaboration with Edgar Froese recorded album Blue Dawn, but it was released only in 2006; also credited for one track on Optical Race (1988) and toured with the band in support of this album).

The band's 1973 album Atem was named as Album of the Year by British DJ John Peel, and this attention helped Tangerine Dream to sign to the fledgling Virgin Records in the same year. Soon afterward they released the album Phaedra, an eerie soundscape that unexpectedly reached #15 in the United Kingdom album charts and became one of Virgin's first bona-fide hits. Phaedra was one of the first commercial albums to feature sequencers and came to define much more than just the band's own sound. The creation of the album's title track was something of an accident; the band was experimenting in the studio with a recently acquired Moog synthesizer, and the tape happened to be rolling at the time. They kept the results and later added flute, bass-guitar, and Mellotron performances. The cantankerous Moog, like many other early synthesizers, was so sensitive to changes in temperature that its oscillators would drift badly in tuning as the equipment warmed up, and this drift can easily be heard on the final recording. This album marked the beginning of the period known as the Virgin Years.

Tangerine Dream are considered a pioneering act in electronic music. Their work with the Ohr electronic music label produced albums that had a pivotal role in the development of the German musical scene known as Kosmische Musik. Their "Virgin Years," so-called because of their association with Virgin Records, produced albums that further explored synthesizers and sequencers, including the UK top 20 albums Phaedra (1974) and Rubycon (1975). The group also had a successful career composing film soundtracks, creating over sixty scores which include those for the films Sorcerer, Thief, Risky Business, The Keep, Firestarter, Legend, Three O'Clock High, Near Dark, Shy People, and Miracle Mile.

Tangerine Dream's earliest concerts were visually simple by modern standards, with three men sitting motionless for hours alongside massive electronic boxes festooned with patch cords and a few flashing Lights. Some concerts were even performed in complete darkness as happened during the performance at York Minster, 20 October 1975. As time went on and Technology advanced, the concerts became much more elaborate, with visual effects, lighting, lasers, pyrotechnics, and projected images. By 1977 their North American tour featured full-scale Laserium effects.

Classical music has had some influence on the sound of Tangerine Dream over the years. György Ligeti, Johann Sebastian Bach, Maurice Ravel, and Arcangelo Corelli are clearly visible as dominant influences in the early albums. A Baroque sensibility sometimes informs the more coordinated sequencer patterns, which has its most direct expression in the La Folia section that comes at the very end of the title track of Force Majeure. In live performances, the piano solos often directly quoted from Romantic classical works for piano, such as the Beethoven and Mozart snippets in much of the late '70s- early '80s stage shows. In the bootleg recording of the Mannheim Mozartsaal concert of 1976 (Tangerine Tree volume 13), the first part of the first piece also clearly quotes from Franz Liszt's Totentanz. The first phrase is played on a harpsichord synthesizer patch, and is answered by the second half of the phrase in a flute voicing on a Mellotron. During the 90s, many releases included recordings of classical compositions: Pictures at an Exhibition (on Turn of the Tides), Largo (from Xerxes) (on Tyranny of Beauty), Symphony in A Minor (by J. S. Bach), and Concerto in A Major / Adagio (by Wolfgang Amadeus Mozart) (both on Ambient Monkeys).

Most of Tangerine Dream's albums are entirely instrumental. Two albums that prominently featured lyrics, Cyclone (1978) and Tyger (1987) were met with disapproval from some fans. While there have occasionally been a few vocals on the band's other releases, such as the track "Kiew Mission" from 1981's Exit and "The Harbor" from 1987's Shy People, the group only recently returned to featuring vocals in a musical trilogy based on Dante's Divine Comedy and their 2007 album Madcap's Flaming Duty.

Throughout the 1980s, Tangerine Dream composed scores for more than twenty films. This had been an interest of Froese's since the late 1960s, when he scored an obscure Polish film, as well as appearing as an actor in several German underground films. He made the score for the experimental film "Never shoot the bathroom man," directed by Jürgen Polland. Many of the group's soundtracks were composed at least partially of reworked material from the band's studio albums or work that was in progress for upcoming albums; see, for Example, the resemblance between the track "Igneous" on their Soundtrack for Thief and the track "Thru Metamorphic Rocks" on their studio release Force Majeure. Their first exposure on U.S. television came when a track for the then in-progress album Le Parc was used as the theme for the television program Street Hawk. Some of the more famous soundtracks have been Sorcerer, Risky Business, Shy People, Thief, Legend, The Keep, Firestarter, Flashpoint and Near Dark.

An infrequently recurring non-musical influence on Tangerine Dream, and Edgar Froese in particular, have been 12th-19th century poets. This was first evident on the 1981 album Exit, the track title "Pilots of the Purple Twilight" being a quote from Alfred Lord Tennyson's poem Locksley Hall. Six years later, the album Tyger featured poems from william Blake set to music; and around the turn of the millennium, Edgar Froese started working on a musical trilogy based on Dante Alighieri's Divine Comedy, completed in 2006. Most recently, the 2007 album Madcap's Flaming Duty features more poems set to music, some again from Blake but also e.g. Walt Whitman.

The band's influence can be felt in ambient artists such as Deepspace, The Future Sound of London, David Kristian, and Global Communication, as well as rock, pop, and dance artists such as Porcupine Tree, M83, DJ Shadow, Ulrich Schnauss, Cut Copy, and Kasabian. The band also clearly influenced 1990s and 2000s Trance music, where lush soundscapes and synth pads are used along with repetitive synth sequences, much like in their 1975 releases Rubycon and Ricochet, as well as some of their music from the early 1980s. The group have also been sampled countless times, more recently by Recoil on the album SubHuman, by Sasha on Involver, and on several Houzan Suzuki albums.

In later years, Tangerine Dream released albums in series. The Dream Mixes series began in 1995 with the last being released in 2010. The Divine Comedy series, based on the writings of Dante Alighieri, spanned 2002-2006. From 2007-2010, the Five Atomic Seasons were released. Most recently, the Eastgate Sonic Poems series, based on the works of famous poetic authors such as Edgar Allan Poe and Franz Kafka, began in 2011, with the last appearing in 2013. Also, beginning in 2007, Tangerine Dream released a number of EPs, referred to as "CupDiscs" by the band.

The group had recording contracts with Ohr, Virgin, Jive Electro, Private Music, and Miramar, and many of the minor soundtracks were released on Varese Sarabande. In 1996, the band founded their own record label, TDI, and more recently, Eastgate. Subsequent albums are today generally not available in normal Retail channels but are sold by mail-order or through online channels. The same applies to their Miramar releases, the rights to which the band bought back. Meanwhile, their Ohr and Jive Electro catalogs (known as the "Pink" and "Blue" Years) are currently owned by Esoteric Recordings.

Tangerine Dream has released over one hundred albums (not counting compilations and fan releases) over the last four decades. A project to collect and release fan concert recordings, known as the Tangerine Tree, was active from 2002 to 2006.

To celebrate their 40th anniversary (1967–2007), Tangerine Dream announced their only UK concert at London Astoria on 20 April 2007. Tangerine Dream also played a totally free open-air concert in Eberswalde on 1 July 2007 and at the Alte Oper in Frankfurt on Main on 7 October 2007. 2008 saw the band in Eindhoven Netherlands playing at E-Day (an electronic music festival); later in the year they also played the Night of the Prog Festival in Loreley, Germany, as well as concerts at the Kentish Town Forum, in London on 1 November, at the Picture House, Edinburgh on 2 November, and their first live concert in the USA for over a decade, at the UCLA Royce Hall, Los Angeles on 7 November.

In 2009 the group announced that they would play a concert at the Royal Albert Hall in London, on 1 April 2010, titled the Zeitgeist concert, 35 years after their milestone concert there on 2 April 1975. The entire concert was released as a 3-CD live album on 7 July 2010.

Tangerine Dream embarked in spring and summer 2012 on a tour of Europe, Canada and the USA called The Electric Mandarine Tour 2012: The 1st leg was a 5-date European tour, beginning on 10 April in Budapest (Hungary) via Padua (Italy), Milano (Italy), Zurich (Switzerland), and ending on 10 May in Berlin (Germany). The 2nd leg was a North-American tour which started with the Jazz Festival in Montréal (Canada) on 30 June, followed by a concert on 4 July at the Bluesfest in Ottawa (Canada) and continued as a 10-date US journey beginning in July in Boston, then New York, Philadelphia, Washington, and California. On 16 November 2014, Tangerine Dream performed in Melbourne, Australia, as part of Melbourne Music Week. They were the final shows with Froese. Tangerine Dream will play two consecutive nights at the Union Chapel, Islington London on April 23 & 24, the second supported by ex Japan and Porcupine Tree musician Richard Barbieri.

On 6 April 2015, the group's remaining members (Thorsten, Ulrich, and Hoshiko) and Bianca Acquaye (Froese's widow), pledged to continue working together in an effort to fulfill Froese's vision for the group. However, ex-member Jerome Froese announced in his Facebook time line that in his opinion Tangerine Dream will not exist without his father.

Tangerine Dream played their first show following Froese's death on 9 June 2016 in Szczecin, Poland.

In September 2017, Tangerine Dream announced the forthcoming release on 29 September 2017 of their new studio album entitled Quantum Gate, coinciding with and celebrating the 50th anniversary of the foundation of the band.