The classical Hasse-Herbrand function is an important object in ramification theory, related to higher ramification groups. In this talk, I will discuss generalizations of the Hasse-Herbrand function and go over some of their properties. These generalized Hasse-Herbrand functions are defined for extensions L/K of complete discrete valuation fields where the residue field k of K is perfect of characteristic p>0 but the residue field l of L is possibly imperfect.