The relentless technology scaling has provided a significant increase in processor performance, but on the other hand, it has led to adverse impacts on system reliability. In particular, technology scaling increases the processor susceptibility to radiation-induced transient faults. Moreover, technology scaling with the discontinuation of Dennard scaling increases the power densities, thereby temperatures, on the chip. High temperature, in turn, accelerates transistor aging mechanisms, which may ultimately lead to permanent faults on the chip. To assure a reliable system operation, despite these potential reliability concerns, fault-tolerance techniques have emerged. Specifically, fault-tolerance techniques employ some kind of redundancies to satisfy specific reliability requirements. However, the integration of fault-tolerance techniques into real-time embedded systems complicates preserving timing constraints. As a remedy, many task mapping/scheduling policies have been proposed to consider the integration of fault-tolerance techniques and enforce both timing and reliability guarantees for real-time embedded systems. More advanced techniques aim additionally at minimizing power and energy while at the same time satisfying timing and reliability constraints. Recently, some scheduling techniques have started to tackle a new challenge, which is the temperature increase induced by employing fault-tolerance techniques. These emerging techniques aim at satisfying temperature constraints besides timing and reliability constraints. This paper provides an in-depth survey of the emerging research efforts that exploit fault-tolerance techniques while considering timing, power/energy, and temperature from the real-time embedded systems’ design perspective. In particular, the task mapping/scheduling policies for fault-tolerance real-time embedded systems are reviewed and classified according to their considered goals and constraints. Moreover, the employed fault-tolerance techniques, application models, and hardware models are considered as additional dimensions of the presented classification. Lastly, this survey gives deep insights into the main achievements and shortcomings of the existing approaches and highlights the most promising ones.