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.

[invited by J.-P. Berrut]