As is well-known, the (0,2) superconformal field theories, in particular the (0,2) Calabi-Yau sigma models, are the natural context for the (geometric) string compactification. In the geometrical setting, these models, however, have received less attention. This was in part because of the assertion that the generic (0,2) Calabi-Yau sigma models suffer from destabilization by the worldsheet instantons which turned out to be not correct for large classes of (0,2) models. The technical difficulty in constructing (0,2) models remained another big obstacle in the study of these models. Witten's gauged linear sigma model (GLSM) approach has dramatically changed the state of affairs. It provided a powerful tool in constructing (2,2) and (0,2) models and in analyzing their 'phase structures'. The (0,2) sigma models that arise in the 'Calabi-Yau phase' of GLSMs are in general singular, whereas their corresponding physical theories axe well-behaved. Therefore, the naive phase picture of the moduli space of such models is not complete and we need to resolve the singularities and consider the moduli space of these desingularized models. Using the methods of toric geometry we have addressed the issue of resolution of singularities. We have also discussed a general framework for the calculation of cohomology groups of twisting sheaves on toric varieties which are important for future works in this direction. In the final part we have worked out some examples.