Fast pulsed discharges are an exciting and growing research topic coinciding with the increasing interest in the creation of non-equilibrium plasmas at atmospheric pressure and in liquids for many applications. The generation of discharges with a voltage pulses having a rise time of 100Vns-1 or higher is of fundamental interest. In gases at elevated pressure the breakdown proceeds in a timescale of several nanoseconds up to microseconds. Changing the applied voltage on the same timescale as the discharge generation allows one to strongly impact plasma parameters and composition. It has been shown by experimental and theoretical studies that higher number densities of reactive species than in classical AC operated plasmas can be formed while maintaining moderate gas temperatures. This is making technological applications such as gas or surface treatment more efficient.