I will discuss my recent joint work with M. Disconzi on the relativistic Euler equations with non-trivial vorticity and entropy. We derived a new formulation of the equations exhibiting miraculous geo-analytic structures, including I) A sharp decomposition of the flow into geometric "wave parts'' and "transport-div-curl parts;" II) Null form source terms; and III) Structures that allow one to propagate one additional degree of differentiability (compared to standard estimates) for the entropy and vorticity. We were inspired to search for such a formulation by Christodoulou's groundbreaking 2007 monograph on shock formation in irrotational and isentropic regions and by related work on the non-relativistic compressible Euler equations. I will then describe how the new formulation can be used to derive sharp results about the dynamics, including results on stable shock formation and the existence of low-regularity solutions. I will emphasize the role that nonlinear geometric optics plays in the framework and highlight how the new formulation allows for its implementation. Finally, I will connect the new formulation to the broader goal of obtaining a rigorous mathematical theory that models the long-time behavior of solutions that can develop shocks.