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This paper aims to review recent literature results on the equilibrium problem and the strengthening design of masonry vaults.

A Lumped Stress Method (LSM) is considered within the Heyman’s safe theorem, based on the definition of thrust surface of a masonry curved structure. In particular, the static problem of the vault is formulated by introducing a membrane continuous of the studied masonry structure to associate with a spatial truss through a nonconforming variational approximation of the thrust surface and membrane stress potential. A tensegrity approach based on a minimal mass design strategy, different strengths in tension and compression of the material is discussed within the strengthening strategy of masonry vaults.

The numerical results have highlighted the efficacy of the two numerical approaches to assess the vulnerability of existing structures and design optimal strengthening interventions of these structures.

The presented models can represent fast and useful tools to assess the vulnerability of existing structures and design optimal strengthening interventions with composite materials of these structures.

The purpose of this paper is to develop and discuss a methodological approach for energy assessment and retrofitting of envelope systems in Mediterranean historical buildings, in order to ensure the desirable balance between improvement requirements and preservation principles.

The methodology is based on the assessment of historical districts at the site, building and component scales, the development of energy models of building-types that are highly representative, in terms of materials, construction techniques, typologies and performances, the identification of intervention priorities and the validation of compatible retrofitting solutions.

The methodology, applied to a representative Adriatic sea town in South Italy, shows the potentialities of innovative materials and technologies (aerogel, PCMs, etc.) as tools to achieve the improvement of the energy performances and the preservation of the original characters. Nevertheless, it shows how the preliminary qualification of the environmental, architectural, constructional and technological characteristics is paramount to support the identification of the current behavior of the building system and the transformation boundaries from the historical values.

The paper proves how assessment and intervention methods and tools, besides effective, compatible, low invasive and durable, should be geocluster oriented and performance based, thus with general reliability for the whole local context and suitable flexibility to be tailored to different specific situations, toward the definition of retrofitting micro-scale measures and macro-scale strategies that are replicable and scalable.