Current mobile devices do not leverage the rich haptic channel of information that our hands can sense, and instead focus primarily on touch based graphical interfaces. Our goal is to enrich the user experience of these devices through bi-directional haptic and tactile interactions (display and control) around the edge of hand-held devices. We propose a novel type of haptic interface, a Haptic Edge Display, consisting of actuated pins on the side of a display, to form a linear array of tactile pixels (taxels). These taxels are implemented using small piezoelectric actuators, which can be made cheaply and have ideal characteristics for mobile devices. We developed two prototype Haptic Edge Displays, one with 24 actuated pins (3.75mm in pitch) and a second with 40 pins (2.5mm in pitch). This paper describes several novel haptic interactions for the Haptic Edge Display including dynamic physical affordances, shape display, non-dominant hand interactions, and also in-pocket ``pull' style haptic notifications. In a laboratory experiment we investigated the limits of human perception for Haptic Edge Displays, measuring the just-noticeable difference for pin width and height changes for both in-hand and simulated in-pocket conditions.