Sadness is generally seen as a negative emotion, a response to distressing and adverse situations. In an aesthetic context, however, sadness is often associated with some degree of pleasure, as suggested by the ubiquity and popularity, throughout history, of music, plays, films and paintings with a sad content. Here, we focus on the fact that music regarded as sad is often experienced as pleasurable. Compared to other art forms, music has an exceptional ability to evoke a wide-range of feelings and is especially beguiling when it deals with grief and sorrow. Why is it, then, that while human survival depends on preventing painful experiences, mental pain often turns out to be explicitly sought through music? In this article we consider why and how sad music can become pleasurable. We offer a framework to account for how listening to sad music can lead to positive feelings, contending that this effect hinges on correcting an ongoing homeostatic imbalance. Sadness evoked by music is found pleasurable: (1) when it is perceived as non-threatening; (2) when it is aesthetically pleasing; and (3) when it produces psychological benefits such as mood regulation, and empathic feelings, caused, for example, by recollection of and reflection on past events. We also review neuroimaging studies related to music and emotion and focus on those that deal with sadness. Further exploration of the neural mechanisms through which stimuli that usually produce sadness can induce a positive affective state could help the development of effective therapies for disorders such as depression, in which the ability to experience pleasure is attenuated.