Surfaces of general type with canonical map of degree d bigger than 8 have bounded geometric genus and irregularity. In particular if d 10 the irregularity is at most 2. In this talk, I will present the existence of surfaces with d = 10 and all possible irregularities, surfaces with d = 12 and irregularities 1 or 2 and surfaces with d = 14 and irregularities 0 or 1. These results together with the construction by C. Rito of a surface with d = 12 and irregularity 0 show that all the possibilities for the irregularity in the cases d = 10, d = 12 can occur, whilst the existence of a surface with d = 14 and irregularity 2 is still an open problem.