The behaviour of a dilute Bose-Einstein Condensate (BEC) trapped in an optical lattice is discussed. The dynamics is described by a discrete nonlinear Schroedinger equation: intrinsically localized excitations, including discrete solitons and breathers, can be created even if the BEC's interatomic potential is repulsive. We present the theoretical analysis of the experimental observation of a Josephson current in an array of weakly coupled BECs [F.S. Cataliotti et al., Science 293, 843 (2001)]. Finally, we discuss the effects of random defects.