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Technological scaling has increased the susceptibility of logic circuits to radiation-induced transient faults, making digital devices less reliable. Although different techniques have been proposed at software, hardware, and hybrid level to mitigate these faults, all of them cause non-negligible overheads in terms of area, energy, and performance. Recently, the use of the approximate computing has taken relevance to minimize the overheads associated with the mitigation of transient faults. The approximate computing paradigm aims to increase the efficiency of a computer system at the expense of accuracy in the results. In this paper we present a review of approximate computing techniques that can be used to reduce the costs in the mitigation of radiation effects at hardware and software levels. In addition, we examine several recent works that have presented promising results in this way.