The special and general theories of relativity are crucial for understanding and modeling cosmic phenomena, as many astrophysical systems operate at the extreme limits of velocity, temperature, density, and gravity. Relativistic effects in these systems not only need to be taken into account, they often dominate a system's structure and evolution. This tutorial will give an introduction to relativistic astrophysics, with particular emphasis on those problems that benefit from complex numerical simulations. The first hour will review relativistic concepts, both special and general, and the crucial role they play in astrophysical systems. The second hour will introduce four or five specific astrophysics challenges, each of which will be dealt with in more detail in later IPAM presentations.