In MTG, do you only discard during your turn? or if you have more than 8 do you discard during someone elses?

When it is my turn and if I had per se 9 cards in MTG, at the end of my turn I would discard down to 7 cards. Say it is my opponents turn and I use an ability that makes me draw a card and now I have 8 cards. At the end of my opponents phase is his discard phase, would I have to discard as well or would I have to wait until my proper turn to discard when that would be my real turn and my actual discard phase?