Since the discovery of the pseudocapacitive behavior in RuO2 by Sergio Trasatti and Giovanni Buzzanca in 1971, materials with pseudocapacitance have been regarded as promising candidates for high-power energy storage. Pseudocapacitance-involving energy storage is predominantly based on faradaic redox reactions, but at the same time the charge storage is not limited by solid-state ion diffusion. Besides the search for pseudocapacitive materials, their implementation into non-aqueous hybrid capacitors stands for the strategy to increase power density by a rational design of the battery structure. Composed of a battery-type anode and a capacitor-type cathode, such devices show great promise to integrate the merits of both batteries and capacitors. Today, the availability of fast-charging technologies is of fundamental importance for establishing electric vehicles on a mass scale. Therefore, from the perspective of materials and battery design, understanding the basics and the recent developments of pseudocapacitive materials and non-aqueous hybrid capacitors is of great importance. With this goal in mind, we introduce here the fundamentals of pseudocapacitance and non-aqueous hybrid capacitors. In addition, we provide an overview of the latest developments in this fast growing research field.