Gamma-ray bursts (GRB’s), short and intense pulses of low-energy $\gamma$ rays, have fascinated astronomers and astrophysicists since their unexpected discovery in the late sixties. During the last decade, several space missions—BATSE (Burst and Transient Source Experiment) on the Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer)—together with ground-based optical, infrared, and radio observatories have revolutionized our understanding of GRB’s, showing that they are cosmological, that they are accompanied by long-lasting afterglows, and that they are associated with core-collapse supernovae. At the same time a theoretical understanding has emerged in the form of the fireball internal-external shocks model. According to this model GRB’s are produced when the kinetic energy of an ultrarelativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circumburst matter. This model has had numerous successful predictions, like the predictions of the afterglow itself, of jet breaks in the afterglow light curve, and of the optical flash that accompanies the GRB’s. This review focuses on the current theoretical understanding of the physical processes believed to take place in GRB’s.

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