In recent years, conformal transformations have been used in a variety of gravitational applications, as well as in other fields. The precise form that these transformations take typically depends on the problem at hand. A brief introduction to the topic of conformal symmetry will lead to a framework from which these applications, such as the mapping of Riemannian spaces and self-similarity, can be put into a broader context. The systematic approach presented suggests a new perspective from which conformal symmetry can be studied. ©1999 American Institute of Physics.