We discuss spatial dispersion effects in three-dimensional discrete metamaterials. In the present work, we consider two examples of metamaterials whose behavior can not be described properly by means of the effective medium model and where nonlocality is important. These examples are (i) discrete structure consisting of the uniaxial dipoles operating in the vicinity of the transition from elliptic to the hyperbolic dispersion regime and (ii) structure composed of isotropic particles with electric polarizability where spatial-dispersion-induced birefringence can arise.