AI alignment considers the overall problem of ensuring an AI produces desired outcomes, without undesirable side effects. While often considered from the perspectives of safety and human values, AI alignment can also be considered in the context of designing and evaluating interfaces for interactive AI systems. This paper maps concepts from AI alignment onto a basic, three step interaction cycle, yielding a corresponding set of alignment objectives: 1) specification alignment: ensuring the user can efficiently and reliably communicate objectives to the AI, 2) process alignment: providing the ability to verify and optionally control the AI's execution process, and 3) evaluation support: ensuring the user can verify and understand the AI's output. We also introduce the concepts of a surrogate process, defined as a simplified, separately derived, but controllable representation of the AI's actual process; and the notion of a Process Gulf, which highlights how differences between human and AI processes can lead to challenges in AI control. To illustrate the value of this framework, we describe commercial and research systems along each of the three alignment dimensions, and show how interfaces that provide interactive alignment mechanisms can lead to qualitatively different and improved user experiences.