Sex determination systems in vertebrates vary along a continuum from genetic (GSD) to environmental sex determination (ESD). Individuals that show a sexual phenotype opposite to their genotypic sex are called sex reversals. Aside from genetic elements, temperature, sex steroids, and exogenous chemicals are common factors triggering sex reversal, a phenomenon that may occur even in strict GSD species. In this paper, we review the literature on instances of sex reversal in fish, amphibians, reptiles, birds, and mammals. We focus on the offspring of sex-reversed parents in the instances that they can be produced, and show that in all cases studied the offspring of these sex-reversed parents exhibit a higher sensitivity to environmental perturbations than the offspring of non-sex-reversed parents. We suggest that the inheritance of this sensitivity, aside from possible genetic factors, is likely to be mediated by epigenetic mechanisms such as DNA methylation, since these mechanisms are responsive to environmental cues, and epigenetic modifications can be transmitted to the subsequent generations. Species with a chromosomal GSD system with environmental sensitivity and availability of genetic sex markers should be employed to further test whether offspring of sex-reversed parents have greater sensitivity to environmental perturbations. Future studies could also benefit from detailed whole-genome data in order to elucidate the underlying molecular mechanisms. Finally, we discuss the consequences of such higher sensitivity in the context of global climate change.