This paper describes the evolution of the SOI MOSFET from single-gate structures to multigate (double-gate, trigate, Pi-gate, Omega-gate and gate-all-around) structures. Increasing the "effective number of gates" improves the electrostatic control of the channel by the gate and, hence, reduces short-channel effects. Due to the very small dimensions of the devices, one-and two-dimensional confinement effects are observed, which results in the need of developing quantum modeling tools for accurate prediction of the electrical characteristics of the devices.