Is there any way of recording your iPhone screen?

Is there any way of taking a video of an iPhone screen (like a screen-capture but a video) or is there any app you could get that would enable this?

You can take a picture of your screen by holding the home button and the power button. However, if you're looking to record activity then you'd have to install software on your phone to see who else is using your phone. You can do a internet search for something like iphone security or surveillance.