  We review some recent developments in mathematical aspects of relativistic
fluids. The goal is to provide a quick entry point to some research topics of
current interest that is accessible to graduate students and researchers from
adjacent fields, as well as to researches working on broader aspects of
relativistic fluid dynamics interested in its mathematical formalism. Instead
of complete proofs, which can be found in the published literature, here we
focus on the proofs' main ideas and key concepts. After an introduction to the
relativistic Euler equations, we cover the following topics: a new
wave-transport formulation of the relativistic Euler equations tailored to
applications; the problem of shock formation for relativistic Euler; rough
(i.e., low-regularity) solutions to the relativistic Euler equations; the
relativistic Euler equations with a physical vacuum boundary; relativistic
fluids with viscosity. We finish with a discussion of open problems and future
directions of research.
