A review is given on some progress made in structural investigation of both synthetic and natural polymers with a view to their degradation. Some new results are presented which stress the importance of the so-called amorphous portion of polymers, and its orientation for processing, properties, and degradation. The structure of polymers determines their accessibility for degrading agents of both chemical and microbial origin. Structure determinations by means of x-rays are therefore an important prerequisite for degradation processes. For thermoplastic products, it is shown that both crystallinity and orientation vary significantly over both the cross section and the distance from the gate. Such changes are reported for polypropylene with a resolution of about 0.02 mm, and their origin is discussed. For regenerated cellulose fibers, structural differences exist between fibers spun according to whether the old viscose process or the new Lyocell process, which is favored on environmental grounds, is used. The kinetics of enzymatic degradation is significantly different for native and regenerated cellulose. An explanation for this finding is proposed.