Since the pioneer work of Hodgekin-Huxley in early 1950s, mathematical models have been employed by neuroscientists and mathematicians

alike to understand the mechanisms governing excitation and propagation of action potentials along neurons. It is a daunting task in view of the complexity of observed phenomena.

A simpler system of FitzHugh- Nagumo equations has been proposed. These latter equations support both standing and traveling waves of action potential. In this talk we will review some works on standing waves of FitzHugh-Nagumo equations. Different methods have been found to be useful for for different physical parameters regime.