We present recent advances in the magnetism and superconductivity of rare earth and uranium compounds. Heavy fermions are formed on the basis of the competition between the RKKY interaction and the Kondo effect in these compounds. The application of pressure to these compounds is useful to control the electronic states in the antiferromagnets CeRh2Si2 and CeRhIn5, and the ferromagnet UGe2. The quadrupole interaction or the quadrupole Kondo effect is found to be responsible for heavy fermions in PrFe4P12. A rich variety of superconducting properties are demonstrated: superconductivity of CeCoIn5 and CeRhIn5 in the vicinity of a quantum critical point, coexistence of ferromagnetism and superconductivity in UGe2, and superconductivity based on the quadrupole fluctuations in PrOs4Sb12, together with the relation between the superconducting transition temperature and the quasi-two dimensionality of the electronic states.