High PAPR signals such as 5G cellular communications present a potential poor trade-off between efficiency and linearity. Power supply modulation is one of several techniques that can avoid this trade-off, and achieve high efficiency and with adequate linearity. This workshop presentation will focus primarily on the polar modulation method for both base-stations and mobile terminals (e.g. smart phones). Circuits for supply modulators will be discussed, and how they can be applied to various classes of microwave power amplifiers (e.g. Class AB, F, etc.). Both analog and digital envelope power modulators will be compared. Linearization methods will be presented tailored to this technique. The challenge of modulation bandwidth limitation will be addressed with several solutions. Finally, multi-carrier systems with potential digital beam steering applications using envelope-of-the-envelope techniques will be shown.