Advances in haptic technologies can alter how real objects feel to our touch and create the experience of haptic augmented reality (AR). However, the definition, use cases, and value to end users of such haptic AR remain unclear. Existing work is concerned with technological implementation and lacks a user-centered perspective. To address these limitations, we analyze haptic AR systems in the literature to understand what constitutes haptic AR, why we would want to alter our sense of touch, and how haptic AR interactions take place. To demonstrate the value of studying haptic AR in the context of real-world tasks and user impressions of the concept itself, we also conducted a small exploratory study with five prototypical applications of different haptic AR systems. Our analysis highlights unexplored areas for haptics and HCI researchers and the need to conduct user evaluations of the overall concept rather than just point examples.