  Fluids can behave in a highly irregular, turbulent way. It has long been
realised that, therefore, some weak notion of solution is required when
studying the fundamental partial differential equations of fluid dynamics, such
as the compressible or incompressible Navier-Stokes or Euler equations. The
standard concept of weak solution (in the sense of distributions) is still a
deterministic one, as it gives exact values for the state variables (like
velocity or density) for almost every point in time and space. However,
observations and mathematical theory alike suggest that this deterministic
viewpoint has certain limitations. Thus, there has been an increased recent
interest in the mathematical fluids community in probabilistic concepts of
solution. Due to the considerable number of such concepts, it has become
challenging to navigate the corresponding literature, both classical and
recent. We aim here to give a reasonably concise yet fairly detailed overview
of probabilistic formulations of fluid equations, which can roughly be split
into measure-valued and statistical frameworks. We discuss both approaches and
their relationship, as well as the interrelations between various statistical
formulations, focusing on the compressible and incompressible Euler equations.
