I will present some recent progress in accelerating N-body simulations of cold dark matter, using temporal COmoving Computer Acceleration (tCOCA, Bartlett, Chiarenza, Doeser & Leclercq 2024) and spatial COmoving Lagrangian Acceleration (sCOLA, Leclercq et al. 2020, Aubin, Leclercq & Lavaux, in prep.). I will then discuss some perspectives.