Long gamma ray bursts (long GRBs) and core-collapse supernovae (CCSNe) are two of the most spectacular explosions in the Universe. They are a focal point of research for many reasons. Nevertheless, despite considerable effort during the last several decades, there are still many fundamental open questions regarding their physics.Long GRBs and CCSNe are related. We know that they are both an outcome of a massive star collapse, where in some cases, such collapse produces simultaneously a GRB and a SN. However, we do not know how a single stellar collapse can produce these two apparently very different explosions. The GRB-SN connection raises many questions, but it also offers new opportunities to learn on the two types of explosions.The focus of the proposed research is on the connection between CCSNe and GRBs, and on the physics of shock breakout. As I explain in this proposal, shock breakouts play an important role in this connection and therefore, I will develop a comprehensive theory of relativistic and Newtonian shock breakout. In addition, I will study the propagation of relativistic jets inside stars, including the effects of jet propagation and GRB engine on the emerging SN. This will be done by a set of interrelated projects that carefully combine analytic calculations and numerical simulations. Together, these projects will be the first to model a GRB and a SN that are simultaneously produced in a single star. This in turn will be used to gain new insights into long GRBs and CCSNe in general.This research will also make a direct contribution to cosmic explosions research in general. Any observable cosmic explosion must go through a shock breakout and a considerable effort is invested these days in large field of view surveys in search for these breakouts. This program will provide a new theoretical base for the interpretation of the upcoming observations.