We present a large set of new self-dual $N=1$ SUSY gauge theories. Examples include $\mathrm{SU}(N)$ theories with tensors and $\mathrm{SO}(N)$ theories with spinors. Using these dualities as starting points, new nontrivial duals can be derived by breaking the gauge group through the Higgs mechanism or by integrating out matter. General lessons that can be learned from these duals are that ``accidental'' infrared symmetries play an important role in duality, many theories have more than one ``dual,'' and there seems to be no simple organizing pattern which relates duals of theories with different number of flavors.