We describe recent extensions and improvements to the advancing front grid generation technique. These improvements target a range of applicability, speed and user friendliness. The range of applicability is enlarged by the ability to produce volumetric grids around thin surfaces (such as shells, membranes, fabrics or surfaces with cusps), the generation of high aspect ratio grids for Navier-Stokes applications, the generation of higher order triangular and tetrahedral elements, and the generation of quadrilateral and hexahedral elements. Speed improvements are the result of reduced search overheads, as well as vectorization and parallelization. User friendliness is enhanced by the ability to grid directly discrete data and simpler ways of specifying the desired element size and shape in space. Numerous examples are included that demonstrate the versatility and maturity that advancing front grid generators have achieved.