## 2 Need for Research  
Despite the plethora of research work conducted and published in the last two decades (Figure 1), modeling and assessment of the seismic vulnerability of masonry structures remains an open issue and, at the same time, a challenge for the practicing civil engineer. Masonry structures are an important part of today's built environment, as it is one of the oldest building systems known to humanity. It is believed to have been in use for over 6000 years and is still in use today in several regions globally. Specifically, in addition to the plethora of important historical structures and monuments which are masonry structures and must be preserved for future generations due to their historical importance, masonry is the most widely used construction type, not only in poverty-stricken countries, due to its low cost compared to the other modern materials, but also in developed countries, due to the aesthetic value that it provides when used in modern constructions. However, it should be highlighted that a common characteristic of all masonry structures is their high seismic vulnerability when subjected to seismic stresses. This is due to the fact that masonry structures are of a brittle and anisotropic nature and, subsequently, each one depicts a distinct brittle and anisotropic behavior. Indeed, masonry is a composite \"material\" that exhibits distinct directional properties, mainly because the mortar joints act as planes of weakness. Figure 1: Evolution of number of publications concerning the masonry materials and structures based on Scopus bibliographic database (28 December 2018). The modeling of the structural behavior, as well as the mechanical characteristics of masonry structures, and the materials comprising it, is still an open issue to this day. The importance of the issue, in addition to the historical values of many masonry structures and of course the safety issues involved, is also linked with economic factors, as approximately 80% of the structural cost from earthquakes is attributable to damage of masonry walls and to the consequent damage of doors, windows, and electrical and hydraulic installations [24]. The intense computational complexity which accompanies such a complex building system is a main problem that must be overcome to successfully accomplish their modeling and assessment in relation to seismic vulnerability and thus successfully protect them by implementing various reinforcement action. For the special case of monumental masonry structures, additional necessary restrictions based on legislations for monument protection, aiming to preserve cultural, artistic, and historical values of the structure, as stated in a series of scientific Charters (e.g., the Athens Charter (1931) [5], the Venice Charter (1964) [6], etc. ), make the process of modeling and restoration even more complex. In addition to the above difficulties, one must also consider the probabilistic nature of earthquakes, which is directly connected and influenced by a significant number of parameters. Thus, due to the high uncertainty of the parameters influencing the behavior of masonry structures, the assessment of their vulnerability cannot be conducted in terms of a deterministic approach. To the contrary, as presented and validated in the following sections, it is suggested to follow a probabilistic approach, which should be applied in cases where the response of the structure is evaluated and compared with limit states, such as specific limit values of response directly interlinked with structural damages. Taking into account the intensely anisotropic nature and behavior of masonry, it would not be an exaggeration to state that masonry material is the mother of all materials (indeed, the word material derives from \(\upmu\upmu\upmu\) in ancient Greek (meeteer), mater in Latin and matar in ancient Hindu, which are all words for \"mother\").