Molecular sieves, including zeolites, distinguish themselves from other sorbents and catalysts by the curvature of the surface (internal pores and cages, and external "pockets") which they offer to incoming molecules on their way to catalytically active sites. Elaborating on the recently proposed general concept of "nesting," this paper attempts to quantify one of its aspects, namely the role of surface curvature when the size of the host structure and that of the guest molecule become comparable. Topics and examples are selected from the literature on physisorption and/or catalysis by zeolites. A simple van der Waals model for the interaction energy and the sticking force of a molecule lodging in a pore is used to rationalize semiquantitatively a number of well-accepted observations, e.g., (i) the role of zeolites as molecular traps; (ii) the origin of the surface barrier postulated to reconcile the large divergence between intracrystalline (self-diffusion) and macroscopically measured (nonequilibrium) diffusion coefficients; (iii) the rapid diffusion of molecules in tight-fitting zeolite pores; (iv) the "window effect" observed for the diffusion of C3C14 linear chain paraffins in erionite; (v) the relationship among apparent acid strength, cracking activity, and molecular "nesting"; and (vi) the dependence of the "constraint index" on temperature. In particular, two new concepts are introduced: the floating molecule which acquires supermobility when its dimension(s) matches closely that of the surrounding channel and the serpentine or creeping motion of the molecule along the channel walls. © 1988.