The well-known capacity of concrete to withstand high temperature and fire is put to the test by the most recent, high-and ultra high-performance cementitious composites, since their more closed pore structure favours pressure build-ups in the pores filled with water, turning to vapour at high temperature. The ensuing spalling phenomena can be prevented by adding polymeric fibres to the mix, while material toughness can be improved – at any temperature – by adding metallic fibres. However, concrete mechanical behaviour depends on the thermal field, which is strictly related to the type of fire and to the thermal properties of the material. Hence, special concretes for special structural applications should be thoroughly characterised at high temperature and after cooling, to evaluate their thermal and mechanical properties. These properties are recalled in the first part of this paper, with reference to thermal diffusivity, compressive and tensile strength, elastic modulus and fracture energy. Furthermore, to maximise the benefits coming from the use of better materials, a parallel rethinking of some aspects of structural analysis is needed. With regard to this point, in the second part of the paper some suggestions and proposals are formulated with reference to the analysis of reinforced concrete sections subjected to combined bending and axial force, and some considerations are made on two rather underrated aspects of the analysis: the role of the thermal self-stresses and the increasing slenderness of fire-exposed columns.