In the Standard Model (SM), the only symmetry broken by the Higgs mechanism is the electroweak symmetry. However, the SM possesses unexplained features suggestive of a more fundamental theory, with additional symmetries broken at a mass scale that is as yet beyond our reach. Two examples are the symmetry between fermions and bosons (supersymmetry) and between leftand right-handed fermion couplings to the weak gauge bosons (left-right symmetry). These models predict additional Higgs bosons that could be observable at the Tevatron. Recent Tevatron searches have probed for neutral Higgs bosons predicted by supersymmetry, and for doubly charged Higgs bosons in left-right symmetric models.