Multilayer structures of Josephson junctions are discussed both in the continuous and the discrete case. For the continuous case some recent results are shown. For two-dimensional shorted arrays, which account for the discrete limit, a model is presented. Analytical and numerical calculations show typical features of coupled sine-Gordon systems such as the splitting of the limit velocity and modes of different symmetry which correspond to the different velocities. The discretization, however, adds interesting features, the most prominent of them being a strong interaction between solitons and discreteness-induced plasma waves.