You're in luck! I used to design drives for brushless motors.
Essentially, you have three vareities of motors with some minor variations:
1 - 3 phase induction motor
2 - 3 phase brushless motor trapazoidal BEMF
3 - 3 phase brushless motor sinusoidal BEMF
The induction motor's driven by a waveform whose voltage
waveform averages out to be a sine wave, though if you look at any phase all you'll see high and low pulses.
Brushless motors use magnets instead of the shorted rotor you find in an induction motor. This gains some efficeincy, and doesn't add all that much cost. Some brushless motors are magnetized such that they produce sine waves as the turn while others produce trapazoidal waves.
The sine wave versions typically have inverters that average a three phase sine wave to drive them. Again, this is the average signal and if you look at the actual signals, they look like pulses.
Most trapazoidal BEMF motors measure and control the current in the windings, so that one pair of windings is on at any given time and that pair has a fairly constant current. The trick then is to know which pair of windings to energize to ensure that the motor is propelled. Some controllers do this by monitoring the shaft position with Hall sensors and other drives monitor the unused winding to determine proper time to switch.
In all of these schemes, you'll have three phases to the motor and six transistors. Currently, the best transistor for low voltage drives, such as 200 volts and less, has proven to be the MOSFET. For higher voltages, all the into 1200 volts, the IBGT is the best. Older drives used SCR's but that technology has been pushed aside for IGBTs, and now even higher voltage applications are beginning to use IGBTs by stacking them.
A few key words: voltage mode control, current mode control, BLDC, vector control, V/F control, sensorless BLDC, IGBT, MOSFET.