Thousands of people are sharing the results of their own experiments with the app on social media.
But since the face-editing tool went viral in the last few days, some have raised concerns over its terms and conditions.
They argue that the company takes a cavalier approach to users' data - but FaceApp said in a statement most images were deleted from its servers within 48 hours of being uploaded.
The company also said it only ever uploaded photos that users selected for editing and not additional images.
What is FaceApp?
FaceApp is not new. It first hit the headlines two years ago with its "ethnicity filters".
These purported to transform faces of one ethnicity into another - a feature that sparked a backlash and was quickly dropped.
The app can, however, turn blank or grumpy expressions into smiling ones. And it can tweak make-up styles.
This is done with the help of artificial intelligence (AI). An algorithm takes the input picture of your face and adjusts it based on other imagery.
This makes it possible to insert a toothy smile, for instance, while adjusting lines around the mouth, chin and cheeks for a natural look.
So what's the problem?
Eyebrows were raised lately when app developer Joshua Nozzi tweeted that FaceApp was uploading troves of photos from people's smartphones without asking permission.
However, a French cyber-security researcher who uses the pseudonym Elliot Alderson investigated Mr Nozzi's claims.
He found that no such bulk uploading was going on - FaceApp was only taking the specific photos users decided to submit.
FaceApp also confirmed to the BBC that only the user-submitted photo is uploaded.
What about facial recognition?
Others have speculated that FaceApp may use data gathered from user photos to train facial recognition algorithms.
This can be done even after the photos themselves are deleted because measurements of features on a person's face can be extracted and used for such purposes.
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