A broad class of kinetic models for molecular motors is given by random walks on quasi 1D lattices with random holding times, not necessarly exponential. We derive information on the asymptotic velocity (law of large numbers), gaussian fluctuations (invariance principle) and large fluctuations (large deviation principle). As applications, we consider some special models and give explicit formulas. We also discuss some theoretical results on Gallavotti-Cohen type symmetries for molecular motors. Joint work with D. Di Pietro, V. Silvestri.