After briefly presenting the history of the problem, we describe the fundamental properties of the nerve cell, its electrical characteristics, and the phenomenological pattern of the excitability phenomenon. We discuss in detail ion transport through biological membranes and models for them, in particular through bilayer lipid membranes. We present the fundamental views on transport mechanisms and discuss the molecular bases of this process. We present the experimental facts concerning the ion channels of biomembranes and describe the theory of single-file ion transport. We discuss in detail the possible physical mechanisms that govern the relationship of the conductivity of the channels to the electric field. We discuss the process of propagation of impulses along nerve fibers.