Selective hearing (SH) refers to the listeners’ capability to focus their attention on a specific sound source or a group of sound sources in their auditory scene. This in turn implies that the listeners’ focus is minimized for sources that are of no interest. This paper describes the current landscape of machine listening research, and outlines ways in which these technologies can be leveraged to achieve SH with computational means. To do so, a brief overview of the state-of-the-art in the fields of detection, classification, separation, localization and enhancement of sound sources is presented, highlighting recent advances in each field, and drawing connections between them. Two main challenges lie ahead in the development of SH applications: (1) Unified methods that can jointly detect/classify/localize and separate/enhance sound sources are required to provide both the flexibility and robustness required for real-life SH. (2) Low-latency methods suitable for real-time performance are critical when dealing with the dynamic nature of real-life auditory scenes.