The cartilage and skin of animals, which are made up of more than fifty per cent water, are rather stiff (having elastic moduli of up to 100 megapascals)1,2as well as tough and hard to break (with fracture energies of up to 9,000 joules per square metre)3,4. Such features make these biological materials mechanically superior to existing synthetic hydrogels. Lately, progress has been made in synthesizing tough hydrogels, with double-network hydrogels achieving the toughness of skin5and inorganic-organic composites showing even better performance6. However, these materials owe their toughness to high stretchability; in terms of stiffness, synthetic hydrogels cannot compete with their natural counterparts, with the best examples having elastic moduli of just 10 megapascals or less7,8,9,10,11. Previously, we described the enzyme-induced precipitation and crystallization of hydrogels containing calcium carbonate, but the resulting materials were brittle12. Here we report the enzyme-induced formation of amorphous calcium phosphate nanostructures that are homogenously distributed within polymer hydrogels. Our best materials have fracture energies of 1,300 joules per square metre even in their fully water-swollen state—a value superior to that of most known water-swollen synthetic materials. We are also able to modulate their stiffness up to 440 megapascals, well beyond that of cartilage and skin. Furthermore, the highly filled composite materials can be designed to be optically transparent and to retain most of their stretchability even when notched. We show that percolation drives the mechanical properties, particularly the high stiffness, of our uniformly mineralized hydrogels.