Relativistic outflows appear in a wide variety of astrophysical sources, from Galactic micro-quasars to cosmological gamma-ray bursts (GRBs) and active galactic nuclei (AGN). In most cases the relativistic outflow is thought to arise from accretion onto a black hole, while neutron-stars are also known to produce relativistic outflows (either in the form of a steady wind or an impulsive ejection of plasmoids). Such relativistic outflow sources are thought to accelerate the highest energy cosmic rays, and are expected to be important sources of high-energy neutrinos and gravitational waves for upcoming detectors. Furthermore, they can probe strong field gravity, large densities and magnetic fields, and may have a strong effect on their environment. Thus, a good understanding of their physics can have many important implications. I plan to study several different aspects of ultra-relativistic outflows, which may help shed light on their underlying physics: (i) the acceleration of an impulsive highly-magnetized relativistic outflow, its interaction with the external medium, as well as the energy dissipation and emission mechanism within the outflow. These have been investigated so far mainly in quasi-steady state long-lived sources, and the differences for impulsive short-lived outflows is of great importance, and particularly relevant for GRBs; (ii) time dependent opacity effects in impulsive relativistic sources – they lead to different observed properties compared to quasi-steady state sources, and probes the emission site and the Lorentz factor of the outflow, and thus its composition (which is very poorly constrained); this is relevant to the prompt gamma-ray emission in GRBs, as well as to flares in Blazars, micro-quasars and GRBs; (iii) The stability properties of relativistic shocks – these develop is relativistic outflow sources and may effect their observed properties, but have not been investigated in much detail so far, as their Newtonian counterparts.