Understanding mechanisms for patterns of electrical activity of neural cells and principles for their selection and control is fundamental for determining how neurons function. After a classical series of papers by Hodgkin and Huxley, nonlinear differential equations became a common framework for modeling neurons. The bifurcation theory for nonlinear ordinary differential equations provides a powerful suite of tools for analyzing neuronal models. Many such models reside near multiple bifurcations. Consequently, in using bifurcation analysis one often encounters rich and complicated bifurcation structure. Therefore, it is desirable to distinguish the universal features pertinent to a given dynamical behavior from the artifacts peculiar to a particular model. This is important in view of the unavoidable simplifications one makes in the process of modeling such complex systems as neural cells, and under the conditions when many parameters are known approximately. The goal of this talk is to describe some general traits of the bifurcation structure for a class of models of excitable cells. They follow from the generic properties of two-dimensional flows near a homoclinic bifurcation. We present a method of reduction of a model of an excitable cell to a one-dimensional map. The bifurcation structure of the system with continuous time endows the map with distinct features: it is a unimodal map with a boundary layer corresponding to the homclinic bifurcation in the original model. The qualitative features of this map account for various periodic and aperiodic regimes and transitions between them. Our approach retains the biophysical meaning of the parameters in the process of reduction, which allows for precise interpretation of various dynamical patterns.