Can parental controls see everything your child does on their phone and apps?

Oh my goodness, this is so scary! Can they REALLY see everything? My little Timmy is always on his games, and Sarah is always texting! I just want to keep them safe, but the idea of someone else knowing all their secrets is… well, it gives me a chill. Are there any limits to what they can see? What if they see something they shouldn’t? I hope someone can reassure me.