Enhancing the thermal performance of building envelopes by improving the thermal properties of construction systems is possible by acting upon not just the insulation level, but also the thermal inertia through proper selection of the construction materials [1–3]. The building structure itself constitutes a source of thermal energy storage and plays a key role in buffering heat and in reducing indoor temperature swings . Literature claims that it is impossible to design energy-efficient buildings using only a U-value-based approach (that is, only with insulation) and that the role of thermal inertia, i.e., the positive effect of thermal capacity, appears to be relevant in particular for moderate climates [5,6].
Historical buildings using stone masonry or rammed earth are characterized by high thermal inertia [7–10]. Studies based on dynamic simulations and on-site monitoring proved that massive envelopes are able to ensure a considerable reduction of indoor thermal discomfort, especially during summer in cooling dominated climates . The use of alveolar bricks or hollow bricks also increases the thermal inertia of buildings compared to tradition brick construction [11,12].
Effect of the addition of thermal inertia (i.e., addition of PCM) in the building envelope 
Modern architecture has moved to more innovative constructions systems using stone masonry or rammed earth. Today, stone is used by many designers to build single layer, multiple layers, composite load-bearing masonry walls, and self-supporting masonry envelopes . Rammed earth construction is also moving towards multi-layers walls (i.e., including insulation)  and considers embodied energy and the use of sustainable materials (i.e., by-products) .
Another addition to modern architectural practices sensitive to the role of thermal inertia is the incorporation of phase change materials (PCM) in walls . When PCM is added to the building envelope, the envelope itself becomes a source of thermal energy storage (TES) and it plays a key role in buffering heat and in mitigating the dynamicity of outdoor thermal oscillations, while displacing the heat penetration in time so that the heat reaches the indoors when it is most needed (peak load reduction and offset). Therefore, the building wall/structure acts as a heat sink during warm/hot periods (and a heat source during cool/cold periods).
Use of sustainable materials in modern rammed earth architecture 
Finally, another material largely studied for its thermal capacity in building envelopes is concrete. Today, studies involve increasing the circularity of concrete by developing new formulations (i.e., geopolymers) [15,16] or adding by-products (i.e., fly ash, steel slag) [17,18] or involve increasing its thermal capacity/inertia by adding PCMs in the concrete formulation [19,20].
This technology is mostly very mature. As seen in the description, stone masonry and rammed earth are construction technologies available in traditional vernacular architecture. In developed countries, this construction materials/systems were substituted by other technologies (i.e., bricks, concrete), but today they are becoming interesting again due to their advantages in terms of climate change mitigation and due to the need of refurbishing the building stock.
On the other hand, the technology using PCM is not as mature, although these materials can be commercially found.
Finally, geopolymers are still in the development stage.