Ambipolar conduction, characterized by a superposition of electron and hole currents, has been observed in many next-generation devices including carbon nanotube, graphene, silicon nanowire, and organic transistors. This paper describes exciting new design opportunities in both analog and digital domains, all of which are inspired by the ability to control ambipolarity during circuit operation. We illustrate this with (i) a single-transistor polarity controllable amplifier, which can greatly simplify communication circuits and (ii) polarity controllable ambipolar logic gates, which are highly expressive yet compact compared to conventional CMOS.