On iPhone there are two legitimate routes, and only one of them shows actual message content.
Route 1 — Apple's own tools, no message content. Screen Time with Family Sharing gives you Communication Limits (who your child can message and when), contact approvals, and app limits. It does not show you the text of the messages, and Apple has deliberately kept it that way. What you can see is metadata: who they contacted, when, and whether a contact was blocked. If your goal is stopping a conversation with a stranger, Communication Limits does that better than reading everything.
Route 2 — Messages in iCloud. Messages is end-to-end encrypted, but if the child's iPhone backs up to iCloud with Messages enabled, the messages are in that backup. With the child's Apple Account credentials and their consent, you can restore that backup to a spare iPhone and read the thread there. This is technically workable and legally clean only with the account holder's knowledge — a 13-year-old's account that you created and administer qualifies; a partner's account does not.
What does not work: any iOS monitoring app that claims to read iMessages live. Apple gives no third-party API for message content, which is why every "iPhone text spy" product either requires the iCloud credentials (Route 2 with a nicer UI) or only works on jailbroken devices. Jailbreaking a child's phone voids its security guarantees and breaks with each iOS update.
A practical middle path: Family Sharing for communication limits, plus a device you administer for deeper visibility. Ultimate Phone Spy covers SMS and messaging on Android, Windows and Mac (sms tracker) — so families with one iPhone and one Android usually put the Android device under the dashboard and leave the iPhone on Apple's controls.
Finally: tell your child what is monitored and why. Kids who know the boundary exists tend to route around it less than kids who discover it later.