Colbert will appear on Meyers's show as a guest. CBS had announced in July that The Late Show would come to an end in May, more than 30 years after its debut in 1993 under David Letterman. It's not just the end of the show. It is the end of the Late Show on CBS. I'm not being replaced this is all just going away, Colbert told his audience in July. A date for the final episode, however, had not been revealed.