  The development of sensible microscopic models is essential to elucidate the
normal-state and superconducting properties of the iron-based superconductors.
Because these materials are mostly metallic, a good starting point is an
effective low-energy model that captures the electronic states near the Fermi
level and their interactions. However, in contrast to cuprates, iron-based
high-$T_{c}$ compounds are multi-orbital systems with Hubbard and Hund
interactions, resulting in a rather involved 10-orbital lattice model. Here we
review different minimal models that have been proposed to unveil the universal
features of these systems. We first review minimal models defined solely in the
orbital basis, which focus on a particular subspace of orbitals, or solely in
the band basis, which rely only on the geometry of the Fermi surface. The
former, while providing important qualitative insight into the role of the
orbital degrees of freedom, do not distinguish between high-energy and
low-energy sectors and, for this reason, generally do not go beyond mean-field.
The latter allow one to go beyond mean-field and investigate the interplay
between superconducting and magnetic orders as well as Ising-nematic order.
However, they cannot capture orbital-dependent features like spontaneous
orbital order. We then review recent proposals for a minimal model that
operates in the band basis but fully incorporates the orbital composition and
symmetries of the low-energy excitations. We discuss the results of the
renormalization group study of such a model, particularly of the interplay
between superconductivity, magnetism, and spontaneous orbital order, and
compare theoretical predictions with experiments on iron pnictides and
chalcogenides. We also discuss the impact of the glide-plane symmetry on the
low-energy models, highlighting the key role played by the spin-orbit coupling.
