My kids have iphones that I now need to have to be able to text and call and do nothing else. Is there anyway to do that? They had iphones that were being inappropriately used and now that I am aware of that usage, I now need to limit all activity.

You can't restrict the phone to only texting and calling, but you can stop them from using the offending apps. Go to Settings > General > Restrictions, and set a restrictions passcode. Then turn off Safari so they can't browse the web, "Installing Apps," and any other desired options. Delete any unwanted third-party apps from their phones, and then they will not be able to re-install them if "Installing Apps" is turned off.

Simply go to Settings>General>Restrictions

Make sure you keep track of your password as it can't be overridden, even by Apple I don't think. (And make sure your kids don't get ahold of the password as that will ruin Upthere point.)

Good luck and good job keeping them accountable!

If you would like to come along side them and keep their browsiing privileges after a while, check out Covenant Eyes in the App Store. It is an alternative to Safari (If they're looking up what I assume they are) that disables private browsing and sends you diagnostics of what they visit.

You could start by disabling eveything but the most basic default apps and then gradually bring back privileges. Teach them how to use their phones and the Internet responsibly and I believe it could pay off in the long run.

EDIT: To answer your question, restrictions would work, but you could wean them back on and have them earn back your trust through the above steps.

Note that using Covenant Eyes with accountability requires an account and you have to pay for the account. However, the browser itself is free.

https://covenanteyes.com/signup/

There are no apps that allow you to monitor the device usage remotely.

Contact your carrier and see if they offer any account monitoring/restriction services. There is usually a monthly fee.