Gamma-ray bursts (GRBs) are the most violent of the known cosmic explosions. They are bright enough to outshine the rest of the gamma-ray universe and can be seen out to the distance of the first generation of stars. The burst of gamma-rays that marks the GRB, which last seconds, is followed by an afterglow - a long-lasting X-ray, optical, and radio emission. GRB exploration was very active during the last two decades, mostly thanks to a continuous observational effort. The theoretical analysis of the observations leads to the understanding that the sources of the prompt and afterglow emission are relativistic jets which are powered by a compact engine. Today we know about two different types of GRBs – long GRBs which are generated by the collapse of a young massive star and short GRBs for which the origin is not confirmed yet. Future planed observing missions (e.g., GLAST) promise that GRBs will remain a focus of astrophysical research in the coming years. As a member of the astrophysics research group in the Tel-Aviv University I plan to address two key topics that I consider as crucial in the way to reveal the physics of GRBs. The first is the physics of relativistic collisionless shocks in unmagnetized plasma and in particular the magnetic field generation in such shocks, as inferred from the observations. In addition for its fundamental physical interest, understanding this topic is a necessary ingredient in order to properly interpret GRB observations. The second topic that I will study is the origin of short GRBs. This is one of the most tantalizing open questions today in high energy astrophysics and its resolution may bear direct implications to the search for gravitational waves. My research objectives will be achieved by a combination of analytical and numerical research, leveraging on the experience I gained during my research in Caltech and the long standing collaborations with theoreticians and observers that I developed while researching in the US.