What technology replaced the rotary phone?

Not sure if you mean on the client end or the phone company end. On the phone company end the move to digital tones instead of number of clicks. On the client end the Touch Tone phone made it's debut in 1963 although both protocols were in place on the phone company end for a very long time.

I just plugged in my 35 year old rotary Bell phone and it worked just fine for sending as well as receiving calls.