The user interface is critical to the success of a diagram recognition system. It is difficult to define precise goals for a user interface, and even more difficult to quantify performance of a user interface. In this paper, we discuss some of the many research questions related to user interfaces in diagram recognition systems. We relate experiences we have gathered during the construction of two on-line diagram recognition systems, one for UML (Unified Modeling Language) notation and the other for mathematical notation. The goal of this paper is to encourage discussion. The graphics recognition community needs strategies and criteria for designing, implementing, and evaluating user interfaces.