\indent Spectral Collocation methods are a powerful set of methods used to solve partial differential equations and ordinary differential equations numerically. This talk will present some of the basic theory behind Spectral Collocation methods, and provide several examples of how they can be utilized. Along the way, we will encounter approximation theory, orders of convergence, wave and soliton equations, and even some nice pictures. No prior knowledge of numerical analysis is assumed; if you are curious about numerical methods but don't have much background, this talk should provide a gentle introduction.