A research project on the deformation capacity of unreinforced masonry structures is underway at the Institute of Structural Engineering of ETH Zurich. The development of the basic building blocks for the displacement-based design of unreinforced masonry structures is the objective of the present research project, which should be seen as a first step in an initiative to investigate the limits of the deformation capacity of unreinforced masonry walls. This paper presents a summary review of previous experimental and analytical studies on the deformation capacity of unreinforced masonry walls subjected to in-plane loading. This review is the first phase of the aforementioned research program. A summary of 71 shear tests on unreinforced masonry walls is presented in the form of a database, along with the statistical analysis and discussion of the tests results. Furthermore, three different computational approaches for structural masonry, i.e. micro-modelling, macro-modelling and macro-element discretization, are discussed, and a review of macro-elements for the in-plane response of unreinforced masonry walls is presented. The reviewed models are discussed and a set of conclusions is given. Special attention is devoted to the deformation capacity parameter throughout the paper. Finally, the paper shows the limitations of our current state of knowledge of the deformation capacity of structural masonry.