With the rise in artificial intelligence (AI)—driven interactive systems, both academics and practitioners within human-computer interaction (HCI) have a growing focus on human-AI interaction. This has resulted in, for example, system-design guidelines and reflections on the differences and challenges when designing for AI-driven interaction as opposed to more-traditional applications. We argue that the current work on human-AI interaction is defined primarily by a focus on what we refer to as intermittent interaction scenarios, in which there is a clear line between the human initiator of an interaction and an almost immediate system response. However, user interaction with AI systems does not necessarily follow this rigid interaction pattern. Inspired by Kristina Höök and Yang et al., we define human-AI interaction as the completion of a user's task with the help of AI support, which may manifest itself in non-intermittent scenarios. By overlooking these other interaction paradigms, we neglect the opportunity to define and support alternative human-AI scenarios. In this article, we present and outline three types of human-AI interaction paradigms, which we refer to as intermittent, continuous, and proactive, highlighting a diverse set of interaction scenarios and pointing to a need for HCI considerations across different types of human-AI interaction. While a wide range of existing AI-powered systems operate continuously in the background of our lives (e.g., step counters, spam filters), these applications do not engage directly with their users. Here, we focus on AI applications that interact directly with their users.