Youla-Kucera (YK) parametrization was formulated decades ago for obtaining the set of controllers stabilizing a linear plant. This fundamental result of control theory has been used to develop theoretical tools solving many control problems ranging from stable controller switching, closed-loop identification, robust control, disturbance rejection, adaptive control to fault tolerant control.This paper collects the recent work and classifies the maccording to the use of YK parametrization, Dual YK parametrization or both, providing the latest advances with main applications indifferent control fields. A final discussion gives some insights on the future trends in the field.