Vivo X20 Plus UD is the first phone in the world to have the fingerprint reader built right into the screen itself. This type of on or in-screen fingerprint reader allows phone manufacturers to create full-screen smartphone without needing to have an extended bottom bezel for it, or have it at the back of the phone which is inconvenient to use.
Now, I've already seen some phone manufacturers putting that fingerprint reader at the right side integrated into one of the side buttons. I actually think it's a good idea and it's very comfortable. However, we don't know how long those buttons will stay there. Furthermore, the arrangement of the button, size and location differ from each phone, so in general it's not a good idea to place it there. You want to have a technology that will work on all future phones and not play with the fingerprint position anytime you design a new mobile device.
From what I've read, this on-screen fingerprint reader is not as responsive as the capacitive fingerprint sensor. I'm sure this will improve in time as well.
Here is a video by 9to5Google that test this under-screen fingerprint sensor to see how it works in practice.
By the way, the sensor was designed by Synaptics. Ovearll, great useful technology that seems very reliable and works fluently.