Ferroelectric wurtzite-type aluminum scandium nitride (Al_1−xSc_xN) presents unique properties that can enhance the performance of non-volatile memory technologies. The realization of the full potential of Al_1−xSc_xN requires a comprehensive understanding of the mechanism of polarization reversal and domain structure dynamics involved in the ferroelectric switching process. In this work, transient current integration measurements performed by a pulse switching method are combined with domain imaging by piezoresponse force microscopy (PFM) to investigate the kinetics of domain nucleation and wall motion during polarization reversal in Al_0.85Sc_0.15N capacitors. In the studied electric field range (from 4.4 to 5.6 MV cm⁻¹), ferroelectric switching proceeds via domain nucleation and wall movement. The currently available phenomenological models are shown to not fully capture all the details of the complex dynamics of polarization reversal in Al_0.85Sc_0.15N. PFM reveals a non-linear increase of both domain nucleation rate and lateral wall velocity during the switching process, as well as the dependency of the domain pattern on the polarization reversal direction. A continuously faster N- to M-polar switching upon cycling is reported and ascribed to an increasing number of M-polar nucleation sites and density of domain walls.