We review recent advances in distributed fiber optic sensing (DFOS) and their applications. The scattering mechanisms in glass, which are exploited for reflectometry-based DFOS, are Rayleigh, Brillouin, and Raman scatterings. These are sensitive to either strain and/or temperature, allowing optical fiber cables to monitor their ambient environment in addition to their conventional role as a medium for telecommunications. Recently, DFOS leveraged technologies developed for telecommunications, such as coherent detection, digital signal processing, coding, and spatial/frequency diversity, to achieve improved performance in terms of measurand resolution, reach, spatial resolution, and bandwidth. We review the theory and architecture of commonly used DFOS methods. We provide recent experimental and field trial results where DFOS was used in wide-ranging applications, such as geohazard monitoring, seismic monitoring, traffic monitoring, and infrastructure health monitoring. Events of interest often have unique signatures either in the spatial, temporal, frequency, or wavenumber domains. Based on the temperature and strain raw data obtained from DFOS, downstream postprocessing allows the detection, classification, and localization of events. Combining DFOS with machine learning methods, it is possible to realize complete sensor systems that are compact, low cost, and can operate in harsh environments and difficult-to-access locations, facilitating increased public safety and smarter cities.