This presentation gives an overview of standard methods for modeling single neurons and small neural networks. Emphasis is placed on explicitly stating the modeling assumptions for each domain. Emphasis is also placed on drawing attention to the commonality of the mathematical methods used in each domain. For instance, the spike generation mechanism within an axon is governed by a nonlinear oscillator. Oscillations at the network level can sometimes be described by the same mathematical formalism even though the underlying physiological mechanism is different. Topics covered will be action potential generation and propagation in the axon of a neuron, signal propagation in the dendritic tree of a neuron, winner-take-all behavior in a small network, and wave propagation across a model of cortical surface.