Although breeding programmes in aquaculture are scarce, and most of them seek increase in productivity by selecting traits such as growth rate, there is a new approach which seeks to select additional traits with economic or production implications; such as flesh quality or stress tolerance. Thus, there are new selection programmes being set up to study stress characteristics with the purpose of defining their genetic nature. In this paper, the estimates of genetic parameters are detailed together with the results of some selection experiments, which have been carried out with different stress-associated characters.