  Recent theoretical advances in the study of heavy ion fusion reactions below
the Coulomb barrier are reviewed. Particular emphasis is given to new ways of
analyzing data, such as studying barrier distributions; new approaches to
channel coupling, such as the path integral and Green function formalisms; and
alternative methods to describe nuclear structure effects, such as those using
the Interacting Boson Model. The roles of nucleon transfer, asymmetry effects,
higher-order couplings, and shape-phase transitions are elucidated. The current
status of the fusion of unstable nuclei and very massive systems are briefly
discussed.
