For the Tinder app in iOS, I assume they are using a pan gesture recognizer on the image view. How is it that another image is shown underneath the image the user has started to
You might want to look at using CollectionViews to implement this. Have a look at https://github.com/petetodd/BGSSwipeChooser
The implementation requires a custom UICollectionViewFlowLayout (example) which can be complex to design, but you get all the good datasource management stuff that comes with CollectionViews.