Recording and analyzing animal sounds, including vocal and non-vocal cues, is a relevant tool to access and monitor different aspects of animal physiology, behaviour and general welfare in a remote, non-invasive and continuous fashion. This field, known as bioacoustics, is considerably growing, notably due to the development of machine learning techniques. Yet, applications of these methods in animal husbandry remain limited, and their potential may not be fully acknowledged. This review aims to present the potential of bioacoustic tools to monitor various aspects of the welfare of farm animals, and focuses on studies published since 2010. The first section of the review introduces the concept of bioacoustics, describes the different parameters that can be extracted from the sounds of animals, and explains how they can be analysed. The potential of these measures to inform about the physical characteristics, individuality, health, physiology, behaviour, and affective states of different species of farm animals are then presented, through a contemporary overview of the research field. Although this analysis identifies a variety of applications of bioacoustics tools in relation to the assessment and monitoring of farm animal welfare, it also points out the current scarcity of methods implemented in practice and available to farm management. Barriers to the development of bioacoustics measures in conventional farming are also discussed, and future directions for this field of research are suggested.