Collision handling is basically part of updating.
There are different approaches to collision handling, so it's best to just try one and see if it works for your situation.
I often tend to update entity positions, then check collision and move the colliding entities to a proper position (i.e. not overlapping) and trigger collision action code. Depending on the game, you might have to run the collision checking code multiple times, in case the re-positioning triggers another collision, but make it a fixed number of times, to not run into an infinite loop.