Neural activity in major depressive disorder and bipolar disorder has been the subject of much debate. Conflicting findings show that cognitive deficits associated with affective disorders can persist beyond remission, and the neural activity associated with such deficits is often inconsistent across different studies. Analytical and theoretical neuroinformatics-based methods (time-series analysis and neural-network modelling) have been used in this thesis to study neural activity associated with depressive illness. My aim was to test whether there are specific structures or networks that are associated with the cognitive function in depression. Further, since depressed patients are often unimpaired during performance of cognitive tasks, I wanted to investigate the neural activity which may underpin compensatory strategies. Three approaches were used to investigate the underlying computational deficit in affective disorders. These can be described as the segregational, integrational and neural-network modelling paradigms. In the first study, I analysed data from mildly-depressed bipolar patients and healthy control subjects performing the Stroop task. I found potential dysfunctional loci, such as the orbito-medial prefrontal cortex, which appears to be vulnerable in bipolar patients and may be normalised when these patients are depressed. Functional connectivity methods were used in the second study to compare task-independent fluctuations between unipolar patients and healthy patients, who showed stronger connectivity between visual and parietal cortices during performance of a memory task. Finally, I used a neural-network approach to study the internal dynamics of an effective connectivity network and subsequently to test different hypotheses regarding both global and localised deficits in depression. These suggested further ways in which networks that involve matching stimuli differ from networks that support working-memory paradigms. The studies in this thesis suggest that depressive illness may be associated with vulnerable links in neuronal-networks associated with cognition and mood. The combination of different paradigms and approaches used highlight the wealth of possibilities that different computational approaches can offer both to data analysis and to the representation and investigation of this data through theoretical modelling.