The results obtained from finite element analysis are significantly af
fected by the quality of elements. In certain applications like shape
optimization, crash analysis, metal forming, fluid flow analysis, and
large displacement analysis, the finite element mesh is systematically
updated in an iterative process. In such situations, in spite of an i
deal starting mesh, the quality of elements could deteriorate, causing
severly distorted elements. In extreme cases, the elements become deg
enerate and further progress of analysis is restricted. An understandi
ng of the methods of quantifying element distortion helps in identifyi
ng 'bad' geometry and in deciding when to remesh. Knowledge about geom
etric configurations which cause degeneracy assists in controlling deg
eneracy during the analysis. This paper contains a survey of available
distortion measures and degeneracy conditions for various elements in
two and three dimensions. It is a review of the literature in this fi
eld in the last two decades. A brief review of rezoning is also includ
ed, since it is one of the more popularly used methods to correct a di
storted mesh.