Anhedonia - a common feature of depression and other neuropsychiatric disorders - encompasses a reduction in the subjective experience and anticipation of rewarding events, and a reduction in the motivation to seek out such events. The presence of anhedonia often predicts or accompanies treatment resistance, and as such better interventions and treatments are important. Yet the mechanisms giving rise to anhedonia are not well understood. In this chapter, we briefly review existing computational conceptualisations of anhedonia. We argue that they are mostly descriptive and fail to provide an explanatory account of why anhedonia may occur. Working within the framework of reinforcement learning, we examine two potential computational mechanisms that could give rise to anhedonic phenomena. First, we show how anhedonia can arise in multi-dimensional drive-reduction settings through a trade-off between different rewards or needs. We then generalise this in terms of model-based value inference and identify a key role for associational belief structure. We close with a brief discussion of treatment implications of both of these conceptualisations. In summary, computational accounts of anhedonia have provided a useful descriptive framework. Recent advances in reinforcement learning suggest promising avenues by which the mechanisms underlying anhedonia may be teased apart, potentially motivating novel approaches to treatment.