It depends on whether the device is Android or iOS. Android devices don’t have to be rooted — iKeyMonitor’s support reps told me that all of the app’s features are fully functional on a non-rooted device. However, iKeyMonitor no longer supports iOS devices that aren’t jailbroken.
If you intend to jailbreak your iOS device, please keep in mind that it can be a very technical process. It will also compromise the phone’s security and, if done incorrectly, may break the phone entirely. Qustodio is an excellent parental control app for iOS that doesn’t require you to jailbreak the device.