The TU-144 entered commercial service with Aeroflot from Moscow to Alma Ata in early 1977.
It was removed from service only seven months later due to unforeseen 'buffeting' in certain conditions.
It also had problems with extremely high fuel consumption because afterburners (reheat) were needed at all times during Supersonic cruise which made it very uneconomical.
Another reason why it was 'retired' is that the aircraft was inordinately noisy from inside and outside - louder than even the Concorde - and that is saying something!
However, in 1995 or so, the TU-144 was ressurected out of an aciatoin museum outside Moscow and, with the help of NASA and Boeing, was put to work by Tupolev as a flying test-bed for a new generation of Supersonic Passenger Jets. However, even this project was dumped in 1998 after the US parties involved, with the exception of NASA, got cold feet.