Peridynamics is a non-local continuum theory which is the base for a meshless computational method particularly suitable for crack propagation simulations. In the original peridynamics formulation computational resources are not used efficiently because a uniform grid with constant horizon on the whole discretized domain is adopted. In the present work we propose adaptive refinement algorithms for the peridynamic grid and apply them to the study of dynamic crack propagation in two dimensional heterogeneous brittle materials. The new computational technique is capable to capture complex phenomena such as crack branching, and other important features as the direction of the propagating cracks in a computationally efficient way. The refinement process is activated by using a new trigger concept based on the damage state of the material. Multiple levels of refinement can be used. Finally several examples of crack propagation are presented, in order to illustrate the potentialities of the proposed algorithms and the good agreement with experimental data.