In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.