Abstract: The remarkable effects associated with superconductivity - e.g. the sudden change in resistance by many orders of magnitude at low temperatures - have stimulated many investigations into the possible use of superconductivity for photon detection dating back at least to the 1930s. However, the practical use of superconducting detectors for astronomy started only in the late 1970s, and ultimately led to the construction of the ALMA interferometer in Chile, the world’s largest ground-based astronomy project. I will briefly review this history before describing our efforts over the past fifteen years to develop a different type of detector based on the superconducting kinetic inductance effect. These kinetic inductance detectors are now being applied for diverse applications in astrophysics across the electromagnetic spectrum, from millimeter to optical wavelengths. I will describe the basic physics as well as some of the practical issues, and will provide examples of instruments currently being developed and potential future applications.