Bidirectional model transformation is a key technology in model-driven engineering (MDE), when two models that can change over time have to be kept constantly consistent with each other. While several model transformation tools include at least a partial support to bidirectionality, it is not clear how these bidirectional capabilities relate to each other and to similar classical problems in computer science, from the view update problem in databases to bidirectional graph transformations. This paper tries to clarify and visualize the space of design choices for bidirectional transformations from an MDE point of view, in the form of a feature model. The selected list of existing approaches are characterized by mapping them to the feature model. Then, the feature model is used to highlight some unexplored research lines in bidirectional transformations.