Singular limits in the theory of partial differential equations represent a class of problems, where some parameters in the equations become small or infinitely large. We discuss the singular limits arising in the scale analysis of energetically isolated fluid systems. In particular, the following topics are addressed: functional analytic framework and the basic ideas of the mathematical theory of continuum fluid mechanics; thermodynamic stability and equilibrium states; low Mach number limits and propagation of acoustic waves in thermally conducting viscous fluids