A central concern in understanding the mechanism for the occurrence of superconductivity in cuprates is the interaction driving the phase transition and their dimensionality. As physical systems near a phase transition have a marked dependence on dimensionality, this can be explored with symples where one of the physical dimensions is reduced and becomes comparable to the correlation length. Recently, it became possible to fabricate sufficiently thin cuprate slabs, revealing a fall of Tc with reduced thickness, becoming pronounced for slabs a few unit cells thick. Related effects have been observed in the YBCO bulk compounds 123, 124 and 247. We analyze the experimental data by invoking finite size scaling and a Ginzburg-Landau treatment. The main conclusions include the following: the fall of Tc with decreasing thickness corresponds to a dimensional crossover, revealing the three-dimensional nature of the interaction mediating superconductivity; there is a predominance of two-dimensional fluctuations and boundaries with reduced thickness; there are crossover phenomena reminiscent of4He films and thin slabs of conventional super-conductors. © 1991 Springer-Verlag.