You put two MOSFETs back-to-back for bidirectional switching - this is how some SSR's work. Triacs are
also common for AC switching, but they don't switch off till the current drops to zero.
Really high power AC equipment uses thyristors or gate-turn-off thyristors which can handle kilovolts and
megawatts. They don't switch nearly as fast as FETs though, but good enough for mains and PWM of large motors.