  I review the Thirring model in 2+1$d$ dimensions, focussing in particular on
possible strongly-interacting UV-stable fixed points of the renormalisation
group, corresponding to a continuous phase transition where a U($2N$) global
symmetry spontaneously breaks to U($N)\otimes$U($N$). Since there is no small
parameter in play, a systematic non-perturbative approach such as numerical
simulation of lattice field theory is mandated. I compare and contrast various
formulations, paying particular attention to models formulated with either
staggered or domain wall lattice fermions. Domain wall fermions, which
faithfully capture U($2N$) symmetry in the limit of wall separation
$L_s\to\infty$, predict a critical flavor number $1<N_c<2$.
