Non-Fermi liquids arise when metals are subject to singular interactions
mediated by soft collective modes. In the absence of well-defined
quasiparticle, universal physics of non-Fermi liquids is captured by
interacting field theories which replace Landau Fermi liquid theory. In this
review, we discuss two approaches that have been recently developed for
non-Fermi liquid theory with emphasis on two space dimensions. The first is a
perturbative scheme based on a dimensional regularization, which achieves a
controlled access to the low-energy physics by tuning the number of
co-dimensions of Fermi surface. The second is a non-perturbative approach which
treats the interaction ahead of the kinetic term through a non-Gaussian scaling
called interaction-driven scaling. Examples of strongly coupled non-Fermi
liquids amenable to exact treatments through the interaction-driven scaling are
discussed.