The article reviews the gap symmetry and structure of Fe-based superconductors, which have recently been discovered and display low-temperature properties suggesting superconducting gap structures that vary significantly among families and even within families as a function of doping or pressure. The authors propose that this nonuniversality can be understood by considering spin fluctuation theory and the peculiar electronic structure of these systems, coupled with the likely "sign-changing s-wave" (s±) symmetry. The review covers theoretical aspects, materials properties, and experimental evidence relevant to this suggestion, and discusses further measurements needed to settle these issues. The Fe-based superconductors, with critical temperatures up to 55K, are compared to cuprates and MgB2, highlighting their similarities and differences in structure, phase diagrams, and normal state properties. The electronic structure of FeBS is discussed, including the limitations of density functional theory (DFT) calculations and minimal band models. The theoretical background on spin fluctuation pairing is reviewed, and the role of disorder in multiband superconductors is explored. The gap symmetry and structure of FeBS are examined, including the possibility of a sign change in the gap and evidence for low-energy subgap excitations. The article concludes by discussing the conceptual importance of FeBS and the challenges and opportunities in understanding high-temperature superconductivity.The article reviews the gap symmetry and structure of Fe-based superconductors, which have recently been discovered and display low-temperature properties suggesting superconducting gap structures that vary significantly among families and even within families as a function of doping or pressure. The authors propose that this nonuniversality can be understood by considering spin fluctuation theory and the peculiar electronic structure of these systems, coupled with the likely "sign-changing s-wave" (s±) symmetry. The review covers theoretical aspects, materials properties, and experimental evidence relevant to this suggestion, and discusses further measurements needed to settle these issues. The Fe-based superconductors, with critical temperatures up to 55K, are compared to cuprates and MgB2, highlighting their similarities and differences in structure, phase diagrams, and normal state properties. The electronic structure of FeBS is discussed, including the limitations of density functional theory (DFT) calculations and minimal band models. The theoretical background on spin fluctuation pairing is reviewed, and the role of disorder in multiband superconductors is explored. The gap symmetry and structure of FeBS are examined, including the possibility of a sign change in the gap and evidence for low-energy subgap excitations. The article concludes by discussing the conceptual importance of FeBS and the challenges and opportunities in understanding high-temperature superconductivity.