How does autofocus on a smartphone work?

[Kookas]

I get how it works in a normal camera, but what about on a phone? My phone's camera clicks audibly when it's focusing, so it must be mechanical, but how do they move the lens in such a small space?

I recorded the sound of the phone focusing on my laptop and amplified it, and it sounds sort of like a spring-loaded door latch, or sometimes like a crisp being eaten.