Autocompletion is an approach that extends and continues partial user input. We propose to interpret autocompletion as a basic interaction concept in human-AI interaction. We first describe the concept of autocompletion and dissect its user interface and interaction elements, using the well-established textual autocompletion in search engines as an example. We then highlight how these elements reoccur in other application domains, such as code completion, GUI sketching, and layouting. This comparison and transfer highlights an inherent role of such intelligent systems to extend and complete user input, in particular useful for designing interactions with and for generative AI. We reflect on and discuss our conceptual analysis of autocompletion to provide inspiration and a conceptual lens on current challenges in designing for human-AI interaction.