Livestock feeding behaviour is an influential research area in animal husbandry and agriculture. In recent years, there has been a growing interest in automated systems for monitoring the behaviour of ruminants. Current automated monitoring systems mainly use motion, acoustic, pressure and image sensors to collect and analyse patterns related to ingestive behaviour, foraging activities and daily intake. The performance evaluation of existing methods is a complex task and direct comparisons between studies is difficult. Several factors prevent a direct comparison, starting from the diversity of data and performance metrics used in the experiments. This review on the analysis of the feeding behaviour of ruminants emphasise the relationship between sensing methodologies, signal processing, and computational intelligence methods. It assesses the main sensing methodologies and the main techniques to analyse the signals associated with feeding behaviour, evaluating their use in different settings and situations. It also highlights the potential of the valuable information provided by automated monitoring systems to expand knowledge in the field, positively impacting production systems and research. The paper closes by discussing future engineering challenges and opportunities in livestock feeding behaviour monitoring.