Optical microresonators confine light to a particular microscale trajectory, are exquisitely sensitive to their microenvironment, and offer convenient readout of their optical properties. Taken together, this is an immensely attractive combination that makes optical microresonators highly effective as sensors and transducers. Meanwhile, advances in material science, fabrication techniques, and photonic sensing strategies endow optical microresonators with new functionalities, unique transduction mechanisms, and in some cases, unparalleled sensitivities. In this progress report, the operating principles of these sensors are reviewed, and different methods of signal transduction are evaluated. Examples are shown of how choice of materials must be suited to the analyte, and how innovations in fabrication and sensing are coupled together in a mutually reinforcing cycle. A tremendously broad range of capabilities of microresonator sensors is described, from electric and magnetic field sensing to mechanical sensing, from single-molecule detection to imaging and spectroscopy, from operation at high vacuum to in live cells. Emerging sensing capabilities are highlighted and put into context in the field. Future directions are imagined, where the diverse capabilities laid out are combined and advances in scalability and integration are implemented, leading to the creation of a sensor unparalleled in sensitivity and information content.