In the US steam locomotives were mostly gone from class I mainline use by 1960. In other countries they remained in use until the 70s and even 80s.

The reason they lasted so long was basically economic. A diesel-electric locomotive cost about twice as much as a steam locomotive, however the diesel is far cheaper to operate and maintain. The average service life of a steam locomotive is about 25 to 30 years. If a railroad bought a new steam locomotive in the early 50s, it could be expected to last well into the 1970s.

Switching to diesels were expensive for railroads. In North America where distances were long, it made sense to change over faster because the cheaper operating cost of diesels and their greater tonnage made for much cheaper costs per mile figures compared to steam. In Europe where trips were shorter and tonnage was more static, diesels had less of an economic advantage. So it made more sense to use up the steam locomotive through their full life expectancy. Also, it was expensive to adapt facilities for diesel and re-train employees.

When mainline steam locomotives disappeared depends on what country you are talking about: the UK ended steam in 1968, eastern Europe in the 1980s, china in the 1990s, the US in the 1960s. But it is all about economics- in the UK for example there were some steam shunting locomotives used around old NCB ( national coal board) coal mines in the early 1980s- the fuel was basically free, there were skilled staff with equipment who could do maintainance on steam locos. It was a cheaper short term measure than buying a new diesel.