I will review recent experimental and theoretical results on the dynamics of Bose-Einstein condensates in periodic optical lattices and in the presence of disorder. I will first discuss the superfluid-insulator transition for a BEC moving in an optical lattice, induced by the occurrence of a dynamical instability. Then I will consider the effect of disorder created by optical speckles on the collective dynamics and the expansion of the condensate. Finally I will discuss the latest results for BECs in bichromatic optical lattices, which are the most promising and versatile tools to investigate localization effects induced by disorder on BECs.