In the last years, there has been a lot of work and results in the area of Numerical Grid Generation; particularly, in the case of Logically Rectangular 2D grids there are new methods whose application leads to good geometric quality meshes. The original goal in generating this kind of grids was to use them to approximate the solution of Partial Differential Equations with Finite-Differences Schemes; however there are relatively few advances in this directions, we can mention the works of Shashkov, Castillo, Steinberg, and Tinoco among others. In this paper we review some of them, present some newer schemes and compare their performance.