Unipolar pulses have a nonzero electric pulse area (integral of the electric field strength with respect of time in a given point of space). Due to unidirectional action on charges they can be an efficient tool for ultrafast control of wave packet dynamics in matter, charges acceleration and so one. In this paper, we briefly revise recent advances (including the results obtained by the authors) in optics of extremely-short unipolar half-cycle pulses.