A proper analysis of thermal desorption spectra (TDS) can give important information about molecular properties of the adsorption system studied (bond energies of heterogeneous adsorption sites and their composition and structure, strengths of adspecies lateral interactions, role of adspecies mobility, etc;); however, this is complicated because all these factors are distributed over the total spectrum. To solve this problem, it is convenient to use a lattice model since this enables us to extend an approach of traditional chemical kinetics for nonideal reactionary systems in such a way that it jointly takes care of surface heterogeneity and adspecies lateral interactions. In this paper, this model is taken as a base to consider fundamental issues of TDS interpretation dealing with a heterogeneous distribution function of adsorption centers over bond energy, on one hand, and the number of peaks and shape of TDS, on the other hand. Moreover, we discuss the validity of phenomenological approaches to interpret TDS; among them are a phenomenological equation employing an effective activation desorption energy and pre-exponential factor and two recently proposed treatments invoking a so-called entropic factor into adsorption-desorption kinetics. In the course of this discussion, we present the molecular description, taking a nonuniform adspecies distribution into account, for the following experimental data: CO/Ru(001), Hg/W(100), and H-2/Ir(110)2 x 1.