Cognitive functions such as attention and memory significantly impact performance in daily life and in various professions, including driving vehicles and providing healthcare services. Driven by the importance of understanding attention, early studies have explored the attentional theories and discovered the attentional boost effect (ABE). In experiments studying the ABE, participants are required to engage in two concurrent tasks: (1) memorising a sequence of briefly displayed stimuli (e.g. images or words) for a later memory test and (2) concurrently detecting a simultaneously presented target signal (e.g. pressing a button when seeing a target white square and taking no action for a distractor black square). Surprisingly, attending to a target boosts memory encoding for the concurrently presented information, contrary to the typical expectation of lowered performance owing to dual-task interference. This effect has been documented not only in behavioural experiments across different materials and modalities but also in neuroimaging investigations. This review paper is divided into several main sections, covering the behavioural evidence supporting the ABE, interpretations of the effect from neuroimaging studies, individual differences, consensus and controversies in ABE research as well as prospective future research in this area. The discussion in this review might also offer helpful insights to researchers for translating this phenomenon into real-world practical applications.