Spectral theory for linear operators has become an important part of functional analysis and operator theory. This text seeks to define a spectrum for nonlinear operators that preserves the useful properties of the linear case, but permits broader applications for nonlinear problems. They compare the properties of spectra for various classes of nonlinear continuous operators, including Fréchet differentiable operators, Lipshitz continuous operators, quasi-bounded operators, and linearly bounded operators. They further examine applications to bifurcation theory, integral equations, and boundary value problems.