Data from the LHC at 7, 8, and 13 TeV, have, so far, yielded no evidence for
new particles beyond the Standard Model Higgs boson. However, the complementary
nature of physics with e$^+$e$^-$ collisions still offers many interesting scenarios
in which new particles can be discovered at the ILC. These scenarios take
advantage of the capability of experiments at e$^+$e$^-$ colliders to observe particles
yielding final states with
missing energy and small mass differences, to observe mono-photon events with
precisely controlled backgrounds, and to observe the full range of exotic decay
modes of the Higgs boson. The searches that an e$^+$e$^-$ collider makes possible are
particularly important for models of dark matter involving a dark sector with
particles of 10--100 GeV mass. In this talk, we will review the opportunities
that the ILC offers for new particle discovery.