  Fundamental physical constants play a profound role in physics. For example,
they govern nuclear reactions, formation of stars, nuclear synthesis and
stability of biologically vital elements. These are high-energy processes
discussed in particle physics, astronomy and cosmology. More recently, it was
realised that fundamental physical constants extend their governing reach to
low-energy processes and properties operating in condensed matter systems,
often in an unexpected way. These properties are those we experience daily and
can routinely measure, including viscosity, thermal conductivity, elasticity
and sound. Here, we review this work. We start with the lower bound on liquid
viscosity, its origin and show how to relate the bound to fundamental physical
constants. The lower bound of kinematic viscosity represents the global minimum
on the phase diagram. We show how this result answers the long-standing
question considered by Purcell and Weisskopf, namely why viscosity never falls
below a certain value. An accompanying insight is that water viscosity and
water-based life are well attuned to fundamental constants, adding another
higher-level layer to the anthropic principle. We then discuss viscosity minima
in liquid He above and below the $\lambda$-point. We subsequently consider a
very different property, thermal diffusivity, and show that it has the same
minimum fixed by fundamental physical constants as viscosity. We also discuss
bounds related to elastic properties, elastic moduli and their analogues in
low-dimensional systems, and show how these bounds are related to the upper
bound for the speed of sound. We conclude with listing ways in which the
discussion of fundamental constants and bounds advance physical theories.

Statistical Mechanics;Materials Science;Soft Condensed Matter