Loop quantum gravity (LQG) is currently one of the most promising approaches to describing general relativity in quantum terms. One of its key issues is to detect in the quantum theory semiclassical states whose macroscopic properties are the same as those of specific configurations of the classical theory. In this dissertation, we begin by presenting the LQG formalism and its physical interpretation. From a mathematical point of view, LQG can be thought of as a canonical quantization of a SU(2) gauge theory in a 3-manifold. However, whereas the usual approach generates a representation exclusively by self-adjoint operators, LQG's polymer approach generates a mixed representation using both self- adjoint and unitary operators. We then take a polymer model, analogous to LQG, of the simplest physical system: the one-dimensional movement of a point particle. In this context, we develop a framework that solves the problem of semiclassical states, which are studied in detail. Finally, we consider the polymer quantization of the free electromagnetic field, which results in an abelian theory which is very similar to LQG. In this context, it is possible to apply the same framework that was developed for the previous case.