In Hong Kong (not Taiwan) most apartment buildings (certainly tall ones) handle waste disposal. There's a trash can in the back stairway on each floor, into which each floor's residents dispose of waste. Granted, there's no mandatory recycling here (one day, we can only hope!) but I imagine it would work the same way, just with more bins.

Sometime during the day people hired by building management bring the trash down and dispose of it in containers or recycling centers.