  We review the phase structure of a three-dimensional, non-compact Abelian
gauge theory (QED3) as a function of the number $N$ of 4-component massless
fermions. There is a critical $N_{c}$ up to which there is dynamical fermion
mass generation and an associated global symmetry breaking. We discuss various
approaches to the determination of $N_c$, which lead to estimates ranging from
$N_c =1$ to $N_c =4$. This theory with N=2 has been employed as an effective
continuum theory for the 2D quantum antiferromagnet where the observed Neel
ordering corresponds to dynamical fermion mass generation. Thus the value of
$N_c$ is of some physical interest. We also consider the phase structure of the
model with a finite gauge boson mass (the Abelian Higgs model).
