  We review several variants of three-dimensional quantum electrodynamics
(QED$_3$) with $N_f$ fermion (or boson) flavors including fermionic (or
spinorial) QED$_3$, bosonic (or scalar) QED$_3$, $\mathcal{N}=1$ supersymmetric
QED and also models of reduced QED (supersymmetric or not). We begin with an
introduction to these models and their flow to a stable infra-red fixed point
in the large-$N_f$ limit. We then present detailed state-of-the-art
computations of the critical exponents of these models within the dimensional
regularization (and reduction) scheme(s), at the next-to-leading order in the
$1/N_f$ expansion and in an arbitrary covariant gauge. We finally discuss
dynamical (matter) mass generation and the current status of our understanding
of the phase structure of these models.
