  Less explored than their metric (Riemannian) counterparts, metric-affine (or
Palatini) theories bring an unexpected phenomenology for gravitational physics
beyond General Relativity. Lessons of crystalline structures, where the
presence of defects in their microstructure requires the use of non-Riemannian
geometry for the proper description of their properties in the macroscopic
continuum level, are discussed. In this analogy, concepts such as wormholes and
geons play a fundamental role. Applications of the metric-affine formalism
developed by the authors in the last three years are reviewed.
