Dan Shechtman was born in 1941 in Tel Aviv, in what was then Mandatory Palestine; the city became part of the new state of Israel in 1948. He grew up in Petah Tikva and Ramat Gan. Shechtman is married to Prof. Tzipora Shechtman, Head of the Department of Counseling and Human Development at Haifa University, and author of two books on psychotherapy. They have a son Yoav Shechtman (a postdoctoral researcher in the lab of W. E. Moerner) and three daughters: Tamar Finkelstein (an organizational Psychologist at the Israeli police leadership center), Ella Shechtman-Cory (a PhD in clinical psychology), and Ruth Dougoud-Nevo (also a PhD in clinical psychology). He is an atheist.

After receiving his Ph.D. in Materials Engineering from the Technion in 1972, where he also obtained his B.Sc. in Mechanical Engineering in 1966 and M.Sc. in Materials Engineering in 1968, Prof. Shechtman was an NRC fellow at the Aerospace Research Laboratories at Wright Patterson AFB, Ohio, where he studied for three years the microstructure and physical metallurgy of titanium aluminides. In 1975, he joined the department of materials engineering at Technion. In 1981–1983 he was on sabbatical at Johns Hopkins University, where he studied rapidly solidified aluminum transition metal alloys, in a joint program with NBS. During this study he discovered the Icosahedral Phase which opened the new field of quasiperiodic crystals.

Linus Pauling is noted saying "There is no such thing as quasicrystals, only quasi-scientists." Pauling was apparently unaware of a paper in 1981 by H. Kleinert and K. Maki which had pointed out the possibility of a non-periodic Icosahedral Phase in quasicrystals (see the historical notes). The head of Shechtman's research group told him to "go back and read the textbook" and a couple of days later "asked him to leave for 'bringing disgrace' on the team." Shechtman felt dejected. On publication of his paper, other Scientists began to confirm and accept empirical findings of the existence of quasicrystals.

From the day Shechtman published his findings on quasicrystals in 1984 to the day Linus Pauling died (1994), Shechtman experienced hostility from him toward the non-periodic interpretation. "For a long time it was me against the world," he said. "I was a subject of ridicule and lectures about the basics of crystallography. The leader of the opposition to my findings was the two-time Nobel Laureate Linus Pauling, the idol of the American Chemical Society and one of the most famous Scientists in the world. For years, 'til his last day, he fought against quasi-periodicity in crystals. He was wrong, and after a while, I enjoyed every moment of this scientific battle, knowing that he was wrong."

In 1992–1994 he was on sabbatical at National Institute of Standards and Technology (NIST), where he studied the effect of the defect structure of CVD Diamond on its growth and properties. Shechtman's Technion research is conducted in the Louis Edelstein Center, and in the Wolfson Centre which is headed by him. He served on several Technion Senate Committees and headed one of them.

Shechtman joined the Iowa State faculty in 2004. He currently spends about five months a year in Ames on a part-time appointment.

A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. "Aperiodic mosaics, such as those found in the medieval Islamic mosaics of the Alhambra palace in Spain and the Darb-i Imam shrine in Iran, have helped Scientists understand what quasicrystals look like at the atomic level. In those mosaics, as in quasicrystals, the patterns are regular -- they follow mathematical rules -- but they never repeat themselves.""An intriguing feature of such patterns, [which are] also found in Arab mosaics, is that the mathematical constant known as the Greek letter tau [sic], or the "golden ratio", occurs over and over again. Underlying it is a sequence worked out by Fibonacci in the 13th century, where each number is the sum of the preceding two."

On January 17, 2014, in an interview with Israel's Channel One, Shechtman announced his candidacy for President of Israel. Shechtman received the endorsement of the ten Members of Knesset required to run. In the elections, held on 10 June 2014, he was awarded only one vote. This led Israeli press and Israeli humorists to qualify Shechtman as "quasi-president" in reference to the "quasi-scientist" quote.