Where is a three phase induction motor used?

Usually in commercial or industrial applications such as water pumps or large air handlers.

A small three horse motor can do a lot of work that a DC motor can...which DC used to be stronger than an AC motor would be. But the changing of voltages via a rectifier isn't always practical. But these days the three phase motors have the same torque and horsepower as a DC motor does.

BUT

Most of your three phase motors these days are controlled by a VFD or variable frequency drive which turns the three phases of AC into DC and then pulses it back to simulate an AC signal of various frequencies other than simply 60Hz and thus the motor can have almost any RPM.

The reason is that motors have a high inductance to them and power companies like to charge extra for a highly inductive power consumption. So when using a VFD all the power company will see is the diodes from the bridge rectifier.