  Sp($2N$) gauge theories with fermonic matter provide an ideal laboratory to
build extensions of the standard model based on novel composite dynamics.
Examples include composite Higgs along with top partial compositeness and
composite dark matter. Without fermions, their study also complements those
based on SU($N_c$) gauge theories with which they share a common sector in the
large $N_c=2N$ limit. We report on our recent progress in the numerical studies
of Sp($2N$) gauge theories discretised on a four-dimensional Euclidean lattice.
In particular, we present preliminary results for the low-lying mass spectra of
mesons and chimera baryons in the theories with $N=2$. We also compute the
topological susceptibility for various values of $N$, extrapolate the results
to the large $N$ limit, and discuss certain universal properties in Yang-Mills
theories.
