[MPaulHolmes]

Torque is proportional to current because there are electromagnets inside the motor, and the stronger the current, the stronger the magnet. Try it with a nail with wire wrapped around it, then connect the wire to a battery. The nail becomes magnetized. The more current flowing through the coils around the nail, the stronger the magnetic field. This is because a moving electric charge causes a magnetic field. The higher the current (the more electrons that are moving) the stronger the magnetic field.

A DC motor basically plays a game of south chasing north (magnetically speaking). Once south reaches its goal of North, the north gets switched to south, and south gets repelled by south, and is attracted to the next north. It keeps switching at just the right time (because of the brushes) so south is always chasing north (and north is always chasing south) around and around in a circle!

Voltage is proportional to speed because the higher the voltage, the faster the current in the coils can switch direction. There's inductance in the coils. It's like momentum. Once the current gets flowing, it doesn't want to stop and flow the other way. You need a lot of pressure in the opposite direction (voltage) to force it to change fast. The faster the current can change, the faster the wheel can spin.

As far as AC motors go, I have no idea how they work! hehe. I would like to learn though.