  We overview the current status of theoretical approaches for heavy-ion fusion
reactions at subbarrier energies. We particularly discuss theoretical
challenges in the coupled-channels approach, that include i) a description of
deep subbarrier hindrance of fusion cross sections, ii) the role of nuclear
dissipation, iii) fusion of unstable nuclei, and iv) an interplay between
fusion and multi-nucleon transfer processes. We also present results of a
semi-microscopic approach to heavy-ion fusion reactions, that combines the
coupled-channels approach with state-of-the-art microscopic nuclear structure
calculations.
