The nervous system is comprised of neurons that transmit electrical and chemical signals. Communication within a neuron is generally via a binary, all or nothing electrical signal called an action potential. On the other hand, communication between neurons is usually a unidirectional chemical signal that is converted to a signed analog electrical signal called a synaptic potential. Neurons are generally envisioned as integrators that temporally summate their inputs in order to decide whether to fire an action potential; however, a better analogy is a nonlinear oscillator. Some neurons are merely excitable whereas others are autogenous oscillators. Circuits of neural oscillators connected by chemical synapses can be modeled as pulse coupled nonlinear oscillators under the assumption that each oscillator returns to its limit cycle between the receipt of successive synaptic inputs. The phase resetting characteristics of the uncoupled oscillators are sufficient to predict the possible phasic relationships that the coupled circuit can exhibit. A discrete map of the time evolution of the circuit can be linearized and analyzed for stability. Thus we can gain valuableinsights about the synchronization behavior of neural ensembles that are hypothesized to serve as substrates for cognition, or in the cases of epilepsy and tremor, to exemplify a "dynamical disease". Another application of this theory is to central pattern generators in which specific phasic relationship between different neural groups are maintained to generate motor patterns such as locomotion and respiration. In some cases a single neuron can also be modeled as a system of coupled oscillators due to distinct spatial compartments within a single neuron.