The controller of a card is the player who originally played it, unless an effect has specified a new controller.
These effects have phrases like “take control” or “put into play under your control”. Cards that refer to “your” cards are always referring to the controller. For example, if a card says “All your characters gain 1 strength”, it affects only characters you control. (For more on handling who controls a card, see “Taking Control of Cards” in the “Advanced Rules” section.)