As artificially intelligent conversational agents (ICAs) become a popular customer service solution for businesses, understanding the drivers of user acceptance of ICAs is critical to ensure its successful implementation. To provide a comprehensive review of factors affecting consumers' adoption and use of ICAs, this study performs a systematic literature review of extant empirical research on this topic. Based on a literature search performed in July 2019 followed by a snowballing approach, 18 relevant articles were analyzed. Factors found to influence human‐machine cognitive engagement were categorized into usage‐related, agent‐related, user‐related, attitude and evaluation, and other factors. This study proposed a collective model of users' acceptance and use of ICAs, whereby user acceptance is driven mainly by usage benefits, which are influenced by agent and user characteristics. The study emphasizes the proposed model's context‐dependency, as relevant factors depend on usage settings, and provides several strategic business implications, including service design, personalization, and customer relationship management.