There are three different types of technologies used by our phones to read your fingerprints:
Capacitive Optical Ultrasonic Capacitive:
A miniature camera is used to take pictures of your finger. These sensors are easy to fool because a good phone can trick those miniature cameras so it may be combined with capacitive sensors to cope with these tricks and to check if there is really a finger there. Sometimes these sensors also support swipes or force sensing.
Ultrasonic:
Ultrasonics is the most advanced form of fingerprint sensor. Mostly, these ultrasonic scanners are used in the medical field to check the pulse. An ultrasonic sound pulse is generated and transmitted to check the pulse. In smartphones, this is used to detect 3D shape of the ridges of the fingerprint.