A review of recent results in the field of short and half-cycle electromagnetic pulses is presented. The sources of their electric area, i.e., the integral of the electric field strength over time, which serves as the main characteristic of extremely short pulses, are revealed. The formation of unipolar and quasi-unipolar pulses under the influence of low-cycle pulses on a quantum dot and on nested quantum wells is analysed. A number of potential applications of unipolar electromagnetic pulses are discussed.