The origin of the renormalization group is re-examined and various applications of the theory are discussed. The attention is focused on the limitations of these methods, and it is found that supplementary conditions are required besides the group equations in order to get unique results. These additional conditions on the solutions form the very basis for whatever physical information one may extract. Therefore, proper attention must be paid to these questions to ensure results which have physical meaning. In many recent applications these aspects have been overlooked, however, and inconsistent assumptions have been introduced. In some cases it is found that the essential results may be obtained under weaker conditions. It remains to be shown that these weaker conditions are consistent with the particular field theory model under consideration.