Yuri Shevchuk, Rustam Asanbaev, Gennady Rodin, Vladimir Sigachev, and Rustam Karimov founded the band in the summer of 1980. Due to a lack of means for recording, the band remained silent until 1982. In the Spring of 1982, the group competed in a contest called Золотой Камертон (or "Golden Tuning Fork"). They won the competition with the song "Не стреляй." In the same year, the group published their first album - Свинья на радуге. After this album was released and the band gained some fame, they attracted the attention of the KGB and their album was declared forbidden. The group was forced to go underground.
As the band's fame grew, so did hostilities from the government. Finding it difficult for the band members to find work in Ufa, Shevchuk moved to Sverdlovsk (now Yekaterinburg) and played with the band Урфин Джюс.
In 1985, Shevchuk moved to Moscow. In March of the same year, he held a concert in Leningrad (now St. Petersburg). In 1987, Shevchuk rebuild the band, now including Nikita Zaitsev, Vadim Kurylev, Andrei Vasiliev, Igor Dotsenko, Andrei Muratov, and Mikhail Chernov. That same year, the band performed in a rock festival in St. Petersburg for a crowd of three thousand people. The band held its first cross-country tour in 1988.
In 1993, DDT was named "best rock group of the year" and Shevchuk was named "best rock-musician of the year."
DDT plays a wide variety of styles, ranging from rock, to country, to blues, and more. They have risen to become one of Russia's most popular and influential rock groups.