The interest in embodying and situating computer programmes took off in the autonomous agents community in the 90s. Today, researchers and designers of programmes that interact with people on human terms endow their systems with humanoid physiognomies for a variety of reasons. In most cases, attempts at achieving this embodiment and situatedness has taken one of two directions: virtual characters and actual physical robots. In addition, a technique that is far from new is gaining ground rapidly: projection of animated faces on head-shaped 3D surfaces. In this chapter, we provide a history of this technique; an overview of its pros and cons; and an in-depth description of the cause and mechanics of the main drawback of 2D displays of 3D faces (and objects): the Mona Liza gaze effect. We conclude with a description of an experimental paradigm that measures perceived directionality in general and the Mona Lisa gaze effect in particular.