Two classes of superconductors have attracted an immense amount of attention, heavy electron (or ”heavy fermion”) superconductors, compounds and more recently, high Tc (superconducting transition temperature), copper oxide superconductors. The behavior and nature of superconductivity in these two classes of materials are reviewed, and the similarities and differences are noted. The heavy electron superconductors CeCu2Si2, UBe13 and UPt3 have low Tc's(<1K) and enormous densities of states N(EF) at the Fermi level E,, as inferred from the coefficient γ of the electronic specific heat Ce=γ(T)T that attains values -J/mole Ce(U)-K^2 at temperature T<1 K. In contrast, the copper oxide superconductors La2-xMxCuO4 (M=Ca, Sr, Ba) and RBa2Cu3O7-δ (R=Y or a rare earth element except for Ce, Pr and Tb) have spectacularly high Tc's that reach -1OOK and relatively small values of N(EF), determined from estimated -y-values of several mJ/mole Cu-K^2. Power law temperature dependences of various superconducting properties indicate that the heavy electron superconductors exhibit anisotropic superconductivity in which the energy gap vanishes at points or lines on the Fermi surface. In analogy with superfluid He, the anisotropic superconductivity may involve triplet-spin pairing of electrons, mediated by paramagnon exchange, a possibility that is supported by recent experiments on the (U1-xThx) Be13 system. The unexpectedly large values of Tc of the copper oxide superconductors suggest that these materials may display an unconventional type of superconductivity, perhaps not unrelated to that of the heavy electron materials. The feature common to the heavy electron and high Tc superconductors may be a magnetic pairing mechanism such as the one incorporated in the resonating valence bond model that was recently advanced by Anderson.