Metals are found frequently in nature and their properties are usually
very well described within Landaus Fermi liquid theory. Various
strongly correlated materials exhibit strange metallic phases which do
not fit into the Fermi-liquid framework, however. The theoretical description
of such non-Fermi liquids remains one of the main unsolved
problems in condensed matter physics. In this talk I will give an
introduction to the problem and show how interesting strongly coupled
field theories arise in the low energy description of such states,
which are still very poorly understood. I will focus on the paradigmatic
problem of a metal coupled to fluctuations of a critical Ising
order parameter and discuss unexpected scaling properties at finite
temperature.