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Emergent electronic phenomena in iron-based superconductors have been at theforefront of condensed matter physics for more than a decade. Much has beenlearned about the origin and intertwined roles of ordered phases, includingnematicity, magnetism, and superconductivity, in this fascinating class ofmaterials. In recent years, focus has been centered on the peculiar and highlyunusual properties of FeSe and its close cousins. This family of materials hasattracted considerable attention due to the discovery of unexpectedsuperconducting gap structures, a wide range of superconducting criticaltemperatures, and evidence for nontrivial band topology, including associatedspin-helical surface states and vortex-induced Majorana bound states. Here, wereview superconductivity in iron chalcogenide superconductors, including bulkFeSe, doped bulk FeSe, FeTe$_{1-x}$Se$_x$, intercalated FeSe materials, andmonolayer FeSe and FeTe$_{1-x}$Se$_x$ on SrTiO$_3$. We focus on thesuperconducting properties, including a survey of the relevant experimentalstudies, and a discussion of the different proposed theoretical pairingscenarios. In the last part of the paper, we review the growing recent evidencefor nontrivial topological effects in FeSe-related materials, focusing again oninteresting implications for superconductivity.

On the Remarkable Superconductivity of FeSe and its Close Cousins