Refinement techniques mostly involve the bisection of mesh edges.
It is a simple procedure which in practice achieves a smoother grading of
the mesh density than is acquired by techniques like the orthogonal
projection of a vertex onto the opposite edge of a triangle.
The reason can be seen easily in two dimensions. If the angles in a
triangular mesh are assumed to be not extremely obtuse, bisection
guarantees that the minimum spacing between mesh points does not decrease
much more pronounced than by a factor of 
and no mesh points lie too
close together. Obtuse angles might be introduced, but could be eliminated
by topological modifications as dicussed later on. Orthogonal projection
avoids bad angles, but even under the assumption of an average element
quality it cannot be guaranteed that mesh points have a sufficient distance.
Too close mesh points induce a high refinement in that region without that
the physical problem calls for it. Self-induced refinement may lead to
convergence problems of the meshing process if not properly addressed as
discussed in Section 6.3.
A new bisection-based refinement method has been introduced by Liu and Joe [92,93]. Interesting research on topics like the longest edge bisection and its ``propagation path'' has been accomplished by Rivara and Hitschfeld [131,132,67]. The order in which several refinement steps are performed has a great effect on the mesh. A lot of research has still to be done in three dimensions.