The awareness of tailings dam safety monitoring has widened due to the recent disasters caused by failures of such structures. The failure rate of tailings dams worldwide (i.e., the percentage of failed dams out of total) is estimated at 1.2%, compared to the 0.01% rate for traditional water dams. Most of the tailings dam monitoring guidelines suggest that the owner develops a robust surveillance program to detect possible indicators of potential failures. This paper presents a thorough review of major guidelines on tailings storage facility (TSF) monitoring and surveillance, the visual parameters to be monitored, as well as good practice in the development of monitoring systems. This paper reviews the recent literature with an emphasis on the development of monitoring systems utilizing sensors, unmanned aerial vehicles (UAVs), and satellite images that may be considered as supplementary guarantees against failure events.