We focus on periodic solutions of the Boussinesq type equations, point out some origins and interesting facts of the equations, and briefly summarize known results of the equations. We will establish local and global existence results for Boussinesq type equations on a circle, employing Fourier series and a fixed point argument, and outline the proofs. At the end we briefly discuss some results regarding periodic solutions of KdV-type equations and Schrodinger type equations.