We expose the past and present state-of-the-art of Micro-ElectroMechanical System (MEMS) inductors. Starting from the basic inductor equations, we discuss the various material and frequency-dependent loss mechanisms that contribute to a decreasing quality factor of an inductive component. We then discuss the most commonly developed inductor geometries: the planar, solenoidal, and stripe inductor. Subsequently, we highlight various techniques to realize RF inductors for operation at GHz frequencies and their integration directly on silicon substrates. We also explain how cheap packaging technologies can be used to realize inductive components that interface directly with silicon chips or can be used for high-sensitivity magnetic field and current sensors. We finally discuss technologies for the realization of power inductors.