Controlling power to a resistive load with AC
It depends what the resistive load is.

If it's a lamp filament, then a phase shift thyristor/triac solution is suitable, as you probably want to avoid flicker.

If it's a heater, with a much longer time constant, then you can use a 'burst fire' controller, to control average power. That switches a number of complete cycles on and off. The benefit of this is it doesn't generate as much electrical interference as switching in the middle of a cycle would.