The aging and lifetimes of polymeric materials depend on the reaction of these materials to the particular stresses which are applied. In many cases the molecular weight of the polymer is changed and this affords a way to follow aging phenomena. In the simplest case a homopolymer is subjected to a stress which increases or decreases its molecular weight without any chemical changes. As the situation becomes more complicated, changes in chemical composition occur and different sized molecular species are generated. These new species may be of extremely low molecular weight or they may be in the form of crosslinked gel. This paper reviews methods which are available for the determination of molecular weight and molecular weight distribution of polymeric materials. Recently developed or modified techniques are treated in more detail. Techniques which may be used to characterize the oligomer region or analyze for the presence of crosslinked gel are included.