Induction motors are practically fixed speed devices. The there is practically only two methods to change the rotation sped of AC induction motor: use frequency converter or use motor with sperate winding for different speeds. In some applciations motors with dual speed winging are used. The applications where accurate speed control is needed, you need s frequency converter. A frequency converter can run a three phase AC motor at very wide speed range quite well (the performance of motor is usually reduced outside it's optimal operation speed).
There are variable frequency drives that allow induction motors to run on different speeds. But on those applications mechanical load and the speed range must be considered, because on those applications motors can get very hot very fast. The problem is that a 60 Hz (or 50 Hz) motor does not have enough iron in it to allow efficient 25 Hz operation. The motor will run hot due to not having enough inductive reactance at the reduced frequency. Dropping down to 10 Hz would make it even worse. A motor designed for variable frequency drive has more iron. Also, it might use a different iron/steel alloy to allow efficient operation at higher frequencies (say 400 Hz). With a light mechanical load and a good motor combined with a good vraible frequency drive controller, it's sometimes possible to get a reasonable speed range using a variable frequency inverter. A good vriable frequency drive device controls both frequency and voltage. The better ones even take into account that at very low speeds the resistance of the coils cannot be negelected. In VFD (variable frequency drive) system the incoming single phase power is rectified and filtered, and three-phase power is generated from the DC rail using three half-bridges. You get to set the frequency over a range so you can vary the speed of your motor, plus a nice digital display etc. It's a bit harder on the motor insulation than just running it from the line, but well-designed motors should be okay. The reason why VFD is hader for motor insulation is that the unductance in the wiring to the motor allows spikes and ringing at the motor itself. The waveforms that go from VFD to motor are typically quite far from ideal sinewave.
Frequency converter does not work with AC induction motors that are run from single phase power source, because the operation of the needed motor phase conversion capacitor is very frequency sensitive (works as expeted only at normal mains frequency).