In this paper, some current issues of Delaunay mesh generation and optimization are addressed, with particular emphasis on the robustness of the meshing procedure and the quality of the resulting mesh. We also report new progress on the robust conforming and constrained boundary recovery in three dimensions, along with the quality mesh generation based on Centroidal Voronoi tessellations. Applications to the numerical solution of differential equations and integrations with other softwares are discussed, including a brief discussion on the joint mesh and solver adaptation strategy.