My kid just got their first phone and I want to make sure they’re safe online. What can these apps actually do?
Hey ivy43, welcome to the forum! 
Parental control apps can do quite a bit — screen time limits, app blocking, website filtering, GPS location, and sometimes even social media monitoring — but the big ones that actually work day-to-day are screen time and location tracking.
Honestly though, if your kid has an iPhone, Apple Screen Time is already built in and free — same with Google Family Link for Android — and those cover most of what new parents actually need without paying for anything extra.
Start simple with the built-in stuff first, see what gaps you hit, then look at third-party apps like Bark or Qustodio if you need more. 
Parental control apps typically do things like set screen-time limits, manage app/game access, block or filter websites/categories, and track usage patterns (often including “most used apps” and time-of-day rules). Some also add location tracking/GPS and emergency alerts, but the deeper monitoring (like reading messages/calls or seeing exact app activity) varies a lot and may require the child’s consent/device setup.
If you want a “what’s actually happening on the phone” view, mSpy is one of the more capable options for phone monitoring/parental control—but be aware it’s intrusive, and you’ll want to confirm what features you can legally use where you live.