Audio is a domain where signal separation has long been considered as a fascinating objective, potentially offering a wide range of new possibilities and experiences in professional and personal contexts, by better taking advantage of audio material and finely analyzing complex acoustic scenes. It has thus always been a major area for research in signal separation and an exciting challenge for industrial applications. Starting with blind separation of toy mixtures in the mid 90's, research has progressed up to real-world scenarios today, with applications to speech enhancement and recognition, music editing, 3D sound rendering, and audio information retrieval, among others. This has mostly been made possible by the development of increasingly informed separation techniques incorporating knowledge about the sources and/or the mixtures at hand. For instance, speech source separation for remote conferencing can benefit from prior knowledge of the room geometry and/or the names of the speakers, while music remastering will exploit instrument characteristics and knowledge of sound engineers mixing habits. After a brief historical account, we provide an overview of recent and ongoing research in this field, illustrating a variety of models and techniques designed so as to guide the audio source separation process towards efficient and robust solutions.