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New developments in superconductivity, particularly through unexpected andoften astonishing forms of superconducting materials, continue to excite thecommunity and stimulate theory. It is now becoming clear that there are twodistinct platforms for superconductivity through natural and syntheticmaterials. Indeed, the latter category has greatly expanded in the last decadeor so, with the discoveries of new forms of superfluidity in artificialheterostructures and the exploitation of proximitization. The former categorycontinues to surprise through the Fe-based pnictides and chalcogenides, andnickelates as well as others. It is the goal of this review to present thistwo-pronged investigation into superconductors, with a focus on those which wehave come to understand belong somewhere between the BCS and Bose-Einsteincondensation (BEC) regimes. We characterize in detail the nature of this``crossover" superconductivity, which is to be distinguished from crossoversuperfluidity in atomic Fermi gases. In the process, we address the multipleways of promoting a system out of the BCS and into the BCS-BEC crossover regimewithin the context of concrete experimental realizations. These involve naturalmaterials, such as organic conductors, as well as artificial, mostlytwo-dimensional materials, such as magic-angle twisted bilayer and trilayergraphene, or gate-controlled devices, as well as one-layer and interfacialsuperconducting films. This work should be viewed as a celebration of BCStheory by showing that even though this theory was initially implemented withthe special case of weak correlations in mind, it can in a very natural way beextended to treat the case of these more exotic strongly correlatedsuperconductors.

When Superconductivity Crosses Over: From BCS to BEC