Russian company Wireless Lab created FaceApp and the app’s terms of condition are a long read. The summary of it is that you give FaceApp irrevocable and royalty-free access to your face. Fair play to them though since most apps do take your data, sometimes without even a notice going as far stealing it.
What’s spectacular about the FaceApp ordeal is that US senator Chuck Schumer has ordered the FBI and FTC to look into the app. So the US does see the app as a major security concern. FaceApp CEO Yaroslav Goncharov has come out and stated that they are not using the pictures for anything questionable. So more than anything, FaceApp’s terms of conditions came off as a cause of concern due to the multiple massive data breaches that have happened in recent time. Reports also point towards the fact that FaceApp isn’t accessing data beyond the single picture you use, with no signs of stealing other sensitive information.
Regardless, it’s best to be safe, especially with external apps like FaceApp. There are already some knockoff FaceApp type apps which do more than just stealing your pictures.