The study of molecules in planetary nebulae is still in its infancy; therefore, it is appropriate both to review existing knowledge and to anticipate developments that will arise as the subject matures. Briefly stated, this subject consists of observations of hydrogen, H2, and carbon monoxide, CO, molecules in a very few nebulae; the tentative identification of the hydrogen molecular ion, H2+; unsuccessful searches for various other species; some theoretical work on molecular processes relevant to planetary nebulae; and the study of molecules in possible precursors of planetary nebulae. Such a facile summary might suggest that molecules are mere curiosities of peripheral interest; on the contrary, it can be asserted that molecular studies of planetary nebulae will yield important new information about their origins, structures, and evolution.