In recent years, neurofeedback has been used as a cognitive training tool to improve brain functions for clinical or recreational purposes. It is based on providing participants with feedback about their brain activity and training them to control it, initiating directional changes. The overarching hypothesis behind this method is that this control results in an enhancement of the cognitive abilities associated with this brain activity, and triggers specific structural and functional changes in the brain, promoted by learning and neuronal plasticity effects. Here, we review the general methodological principles behind neurofeedback and we describe its behavioural benefits in clinical and experimental contexts. We review the non-specific effects of neurofeedback on the reinforcement learning striato-frontal networks as well as the more specific changes in the cortical networks on which the neurofeedback control is exerted. Last, we analyse the current challenges faces by neurofeedback studies, including the quantification of the temporal dynamics of neurofeedback effects, the generalisation of its behavioural outcomes to everyday life situations, the design of appropriate controls to disambiguate placebo from true neurofeedback effects and the development of more advanced cortical signal processing to achieve a finer-grained real-time modelling of cognitive functions.