Despite the omnipresence of clay brick as construction material since thousands of years, fundamental knowledge about the link between composition, microstructure, and mechanical performance is still scarce. In this paper, we use a variety of advanced techniques of experimental mechanics and material characterization for extruded clay brick for masonry, that range from scanning electron microscopy (SEM) coupled with energy-dispersive X-ray spectroscopy, mercury intrusion porosimetry, to instrumented nanoindentation and macroscopic strength and durability tests. We find that extruded clay brick possesses a hierarchical microstructure: depending on the firing temperature, a "glassy'' matrix phase, which manifests itself at submicrometer scales in form of neo-crystals of mullite, spinel-type phase, and other accessory minerals, forms either a granular or a continuum matrix phase that hosts at submillimeter scale the porosity. This porous composite forms the backbone for macroscopic material performance of extruded brick, including anisotropic strength, elasticity, and water absorption behavior.