Actinides, the heavy radioactive elements at the frontier of the periodic table, will be the backbone of next-generation nuclear power applications. Yet, advancing our understanding of their basic chemical and physical properties to a level that equals that of the lighter chemical elements is mandatory for a science-based safety assessment of the reactors of the future. Present efforts on the physics side are focused on unraveling the "correlated electron" problem by the combined use of novel spectroscopies and novel theoretical tools going beyond band theory and atomic multiplet physics. Unexpected new states of quantum matter have been found in actinide systems, for instance, topologically protected insulator behavior with gapless Dirac fermion states on the surface or exotic superconducting states in proximity to valence or magnetic quantum critical points. At the same time, several basic assumptions in the area of actinide chemistry, including reductive chemistry and bond-length analysis, are being questioned, suggesting that much new chemistry involving actinides is awaiting discovery. This session presents the state-of-the-art science behind this partially unexplored frontier of chemistry and physics.