Integration of superconducting nanowire single-photon detectors with nanophotonic waveguides is a key technological step that enables a broad range of classical and quantum technologies on chip-scale platforms. The excellent detection efficiency, timing and noise performance of these detectors have sparked growing interest over the last decade and have found use in diverse applications. Almost 10 years after the first waveguide-coupled superconducting detectors were proposed, here, we review the performance metrics of these devices, compare both superconducting and dielectric waveguide material systems and present prominent emerging applications.