  Although the existence of nematic order in iron-based superconductors is now
a well-established experimental fact, its origin remains controversial. Nematic
order breaks the discrete lattice rotational symmetry by making the $x$ and $y$
directions in the Fe plane non-equivalent. This can happen because of (i) a
tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking
of an orbital symmetry, or (iii) a spontaneous development of an Ising-type
spin-nematic order - a magnetic state that breaks rotational symmetry but
preserves time-reversal symmetry. The Landau theory of phase transitions
dictates that the development of one of these orders should immediately induce
the other two, making the origin of nematicity a physics realization of a
"chicken and egg problem". The three scenarios are, however, quite different
from a microscopic perspective. While in the structural scenario lattice
vibrations (phonons) play the dominant role, in the other two scenarios
electronic correlations are responsible for the nematic order. In this review,
we argue that experimental and theoretical evidence strongly points to the
electronic rather than phononic mechanism, placing the nematic order in the
class of correlation-driven electronic instabilities, like superconductivity
and density-wave transitions. We discuss different microscopic models for
nematicity in the iron pnictides, and link nematicity to other ordered states
of the global phase diagram of these materials -- magnetism and
superconductivity. In the magnetic model nematic order pre-empts stripe-type
magnetic order, and the same interaction which favors nematicity also gives
rise to an unconventional $s^{+-}$ superconductivity. In the charge/orbital
model magnetism appears as a secondary effect of ferro-orbital order, and the
interaction which favors nematicity gives rise to a conventional $s^{++}$
superconductivity.
