Over the last several decades, many mesh generation methods, and a plethora of corresponding adaptive methods for solving differential equations, have been developed. In this talk, we describe a simple framework for describing most of these methods which is based upon the mesh equidistribution and alignment principles. We focus on two general types of methods, those based upon a variational formulation of the mesh generation problem and those which solve some version of the optimal mass transport problem, a problem in which there has been considerable research interest of late.