The "Delete" button used to remove entries from your iPhone's call history becomes visible when you enter the list's editing mode. From within that mode, you can also clear the entire history instead of deleting calls one by one. This process works in iOS 8.1, the most recent version at the time of publication, but it also works the same way in all recent versions of iOS, starting from version 6 onwards.
Tap the red "Minus" button by a call to show the Delete button.
Tap the "Delete" button to remove that call from the call history.
Repeat the process for every other call you want to remove and then tap "Done."
Tap "Clear All Recents" to confirm the deletion.
Tips & Warnings
- To delete a single entry from the call history, you can also swipe over it to expose the "Delete" button. Tap "Missed" to filter the call history to only show missed calls.
- The process described in the second section clears your entire call history, whether you are looking at the entire list or filtering it to only missed ones. If you want to remove only missed calls, the only way is to delete each of them individually.
- The only way to recover a deleted call history is to restore your iPhone to a recent backup, but you will lose anything that changed since you made that backup.