In Nature, organisms from all five kingdoms are well known to produce a wide range of mineralized tissues combining inorganic and organic materials that are used for a large number of functions. Examples are shells and coral skeletons that give protection for the animals, magnetic particles in bacteria used for navigation and vertebrate bone that provide mechanical support and protection for the body. In all cases, the precipitation and crystallisation of the inorganic materials are controlled by the cells, resulting in mineralized tissues with extraordinary morphologies and remarkable mechanical properties. Our research is aimed at understanding how organisms control the formation of such mineralized tissues, and how their properties arise from their structures. In this talk I will discuss our work on two model systems: unicellular marine algae called coccolithophores that produce scales of calcium carbonate in the form of calcite, and shells of brachiopods that are made of calcium phosphate in the form of fluorapatite. On coccolithophores, I will present our research on the dynamics of calcium storage and transport inside the cell as well as their strategies to control crystal nucleation and morphology. On the brachiopod shells, I will present our research on their structure and material properties, in particular how they reversibly switch between hard and brittle when dry to soft and flexible when hydrated. Such adaptability in mechanical properties as a function of hydration is unprecedented in biological organic inorganic composites, and can provide inspiration for the development of new materials for advanced applications.