Given a collection of points, edges, and faces, in a bounded region
$\Omega \subset \Re^d$, the meshing problem is to construct the
coarsest possible triangulation of $\Omega$ from tetrahedra having
bounded aspect ratio which ``conforms'' to the input. These
requirements can lead to very complicated algorithms; so much so that
it can be difficult to verify correctness. I will give an overview of
the ideas and issues that arise when constructing algorithms to solve
the meshing problem, and will indicate how the mesh generation problem
touches on many areas of mathematics and computer science such as
approximation/interpolation theory, computational geometry, sphere
packing, graph theory, algorithm design.