A fact that has been neglected in most theories of brittle fracture is that the elasticity of a solid clearly depends on its state of deformation. Metals will weaken, or soften, and polymers stiffen as the strain approaches the state of materials failure. It is only for infinitesimal deformation that the elastic moduli can be considered constant and the elasticity of the solid linear. We show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture and that linear theory is incapable of capturing all phenomena. We introduce a new concept of a characteristic length scale ξ for the energy flux near the crack tip and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale. The new length scale ξ, heretofore missing in the existing theories of dynamic fracture, helps to form a comprehensive picture of crack dynamics, explaining super-Rayleigh and supersonic fracture. We further address the stability of cracks, and show agreement of the Yoffe criterion with the dynamics of cracks in harmonic systems. We find that softening hyperelastic effects lead to a decrease in critical instability speed, and stiffening hyperelastic effects leads to an increase in critical speed. The main conclusion is that hyperelasticity plays a critical role in forming a complete picture of dynamic fracture.