We present recent results on lattice gauge theories with fermions in
higher-dimensional representations of the gauge group. In particular
we focus on numerical studies of quenched SU(N) at large N, and SU(2)
with two flavours of dynamical fermions in two-index
representations. We describe the generalization of the existing
algorithms to handle arbitrary representations and discuss the scope
of such simulations. We show preliminary results for the meson
spectrum of these theories, and analyze their relevance for
strongly-interacting dynamics beyond QCD.