Raman-based distributed temperature sensors are now used in a wide variety of industrial and scientific applications. In this paper, we set out the physical principles behind these systems and we summarise the many approaches to their design, the relevant parameters, and the significant features of employed schemes such as optical time- or frequency-domain reflectometry, with resulting implications for their performance. Recent techniques aimed at enhancing the sensing performance or overcoming known issues are also addressed such as photon counting or pulse coding. Also, current standardisation efforts are mentioned, and important applications of the technology are reviewed.