In the last decades we have witnessed a significant advance in protein folding study and several theoretical models have been proposed with the aim to elucidate the relationship between protein folding kinetics and the structure of the native state (the functional state of the protein). One of these, introduced in 1978 by Wako and Saito and later reconsidered by Munoz and Eaton, is based on a lattice statistical mechanical model with remarkable mathematical properties which make it possible to obtain exact results. In my talk I am going to discuss the Wako-Saito-Munoz-Eaton model of protein folding and its properties. I will begin illustrating equilibrium ones and then, using these as a starting point, I will propose a way to treat the kinetic problem that allows to reduce the computational complexity to polynomial, from exponential in the number of aminoacids of the protein, and makes it possible to obtain good semi-analytical approximation of its exact solution. An application of exposed methods to the B domain of Staphylococcal protein A kinetics will be considered. Because of its fast kinetics, this protein has been a target of many works but none of the published atomistic simulations are fully consistent with the experimental picture although many capture important features. Dependence of the relaxation rate and equilibrium topics on denaturant concetration will be showed in a comparison with experimental results. The presentation will end up with a study of the relationship between equilibration rate and native topology for some model structures. Several attempts have been made to find functional relationships between experimentally determined rates and measures of structural properties of the native state. In the original proposal by Plaxco, Simons and Baker the relative contact order was introduced and shown to correlate with the logarithm of the folding rate, while no significant correlation was found using the stability or the length. A similar good correlation was obtained by Jackson, considering the absolute contact order. This last one will be discussed in the context of the model for a class of ideal beta-sheets.