Sounds in everyday life seldom appear in isolation. Both humans and machines are constantly flooded with a cacophony of sounds that need to be sorted through and scoured for relevant information—a phenomenon referred to as the ‘cocktail party problem’. A key component in parsing acoustic scenes is the role of attention, which mediates perception and behaviour by focusing both sensory and cognitive resources on pertinent information in the stimulus space. The current article provides a review of modelling studies of auditory attention. The review highlights how the term attention refers to a multitude of behavioural and cognitive processes that can shape sensory processing. Attention can be modulated by ‘bottom-up’ sensory-driven factors, as well as ‘top-down’ task-specific goals, expectations and learned schemas. Essentially, it acts as a selection process or processes that focus both sensory and cognitive resources on the most relevant events in the soundscape; with relevance being dictated by the stimulus itself (e.g. a loud explosion) or by a task at hand (e.g. listen to announcements in a busy airport). Recent computational models of auditory attention provide key insights into its role in facilitating perception in cluttered auditory scenes.This article is part of the themed issue ‘Auditory and visual scene analysis’.