There is a considerable public and scientific debate concerning welfare of fish in aquaculture. In this review, we will consider fish welfare as an integration of physiological, behavioral, and cognitive/emotional responses, all of which are essentially adaptative responses to stressful situations. An overview of fish welfare in this context suggests that understanding will rely on knowledge of all components of allostatic responses to stress and environmental perturbations. The development of genomic technologies provides new approaches to this task, exemplified by how genome-wide analysis of genetic structures and corresponding expression patterns can lead to the discovery of new aspects of adaptative responses. We will illustrate how the genomic approach may give rise to new biomarkers for fish welfare and also increase our understanding of the interaction between physiological, behavioral, and emotional responses. In a first part, we present data on expression of candidate genes selected a priori. This is a common avenue to develop molecular biomarkers capable of diagnosing a stress condition at its earliest onset, in order to allow quick corrective intervention in an aquaculture setting. However, most of these studies address isolated physiological functions and stress responses that may not be truly indicative of animal welfare, and there is only rudimentary understanding of genes related to possible cognitive and emotional responses in fish. We also present an overview on transcriptomic analysis related to the effect of aquaculture stressors, environmental changes (temperature, salinity, hypoxia), or concerning specific behavioral patterns. These studies illustrate the potential of genomic approaches to characterize the complexity of the molecular mechanisms which underlies not only physiological but also behavioral responses in relation to fish welfare. Thirdly, we address proteomic studies on biological responses to stressors such as salinity change and hypoxia. We will also consider proteomic studies developed in mammals in relation to anxiety and depressive status which may lead to new potential candidates in fish. Finally, in the conclusion, we will suggest new developments to facilitate an integrated view of fish welfare. This includes use of laser microdissection in the transcriptomic/proteomic studies, development of meta-analysis methods for extracting information from genomic data sets, and implementation of technological advances for high-throughput proteomic studies. Development of these new approaches should be as productive for our understanding of the biological processes underlying fish welfare as it has been for the progress of pathophysiological research.