High pressure can strongly influence the electronic properties of a metal, by modifying either the shape or the topology of its Fermi surface (FS). In the case of low-dimensional anisotropic superconductors, typified by high-T_c cuprates, some quasi-2D organic salts and heavy-fermion compounds, we show that the occurrence of an electronic topological transition is generic to a non-monotonic pressure dependence of the critical temperature T_c. On the other hand, a change in shape of the FS can be correlated with the steady increase of T_c as a function of the ratio between next-nearest-and nearest-neighbour hopping, as is observed in the high-T_c cuprates.