Summary: We propose a computational method for a homogenized peridynamics description of fiber-reinforced composites and we use it to simulate dynamic brittle fracture and damage in these materials. With this model we analyze the dynamic effects induced by different types of dynamic loading on the fracture and damage behavior of unidirectional fiber-reinforced composites. In contrast to the results expected from quasi-static loading, the simulations show that dynamic conditions can lead to co-existence of and transitions between fracture modes; matrix shattering can happen before a splitting crack propagates. We observe matrix-fiber splitting fracture, matrix cracking, and crack migration in the matrix, including crack branching in the matrix similar to what is observed in recent dynamic experiments. The new model works for arbitrary fiber orientation relative to a uniform discretization grid and also works with random discretizations. The peridynamic composite model captures significant differences in the crack propagation behavior when dynamic loadings of different intensities are applied. An interesting result is branching of a splitting crack into two matrix cracks in transversely loaded samples. These cracks branch as in an isotropic material but here they migrate over the “fiber bonds”, without breaking them. This behavior has been observed in recent experiments. The strong influence that elastic waves have on the matrix damage and crack propagation paths is discussed. No special criteria for splitting mode fracture (Mode II), crack curving, or crack arrest are needed, and yet we obtain all these modes of material failure as a direct result of the peridynamic simulations.