In this chapter we consider the mechanisms involved in cognitive control - from both a computational and a neurobiological perspective - and how these might be impaired in schizophrenia. By 'control', we mean the ability of the cognitive system to flexibly adapt its behaviour to the demands of particular tasks, favouring the processing of task-relevant information over other sources of competing information, and mediating task-relevant behaviour over habitual, or otherwise prepotent responses. There is a large body of evidence to suggest that the prefrontal cortex (PFC) plays a critical role in cognitive control. In previous work, we have used a computational framework to understand and develop explicit models of this function of PFC, and its impairment in schizophrenia. This work has lead to the hypothesis that PFC houses a mechanism for representing and maintaining context information. We have demonstrated that this mechanism can account for the behavioural inhibition and active memory functions commonly ascribed to PFC, and for human performance in simple attention, language and memory tasks that draw upon these functions for cognitive control. Furthermore, we have used our models to simulate detailed patterns of cognitive deficit observed in schizophrenia, an illness associated with marked disturbances in cognitive control, and well established deficits of PFC. Here, we review results of recent empirical studies that test predictions made by our models regarding schizophrenic performance in tasks designed specifically to probe the processing of context. These results showed selective schizophrenic deficits in tasks conditions that placed the greatest demands on memory and inhibition, both of which we have argued rely on the processing of context. Furthermore, we observed predicted patterns of deterioration in first episode vs multi-episode patients. We also discuss recent developments in our computational work, that have led to refinements of the models that allow us to simulate more detailed aspects of task performance, such as reaction time data and manipulations of task parameters such as interstimulus delay. These refined models make several provocative new predictions, including conditions in which schizophrenics and control subjects are expected to show similar reaction time performance, and we provide preliminary data in support of these predictions. These successes notwithstanding, our theory of PFC function and its impairment in schizophrenia is still in an early stage of development. We conclude by presenting some of the challenges to the theory in its current form, and new directions that we have begun to take to meet these challenges. In particular, we focus on refinements concerning the mechanisms underlying active maintenance of representations within PFC, and the characteristics of these representations that allow them to support the flexibility of cognitive control exhibited by normal human behaviour. Taken in toto, we believe that this work illustrates the value of a computational approach for understanding the mechanisms responsible for cognitive control, at both the neural and psychological levels, and the specific manner in which they break down in schizophrenia.