Fermi surface properties in rare earth (R) and actinide (An) compounds of RX3 (X: Al, Ga, In, Si, Ge, Sn, Pb), AnX(3), RTIn5 (T: transition metal), and AnTGa(5) are clarified as a function of the number of valence electrons. The electronic state can be changed by applying pressure and magnetic field. A change of Fermi surface properties associated with the metamagnetic behavior and the quantum critical point is also clarified precisely, together with the split Fermi surfaces in the non-centrosymmetric crystal structure, and the de Haas-van Alphen oscillations in the superconducting mixed state. In the quantum critical point region, the conduction electrons, or quasi-particles, are of an f-electron character, with heavy effective masses of 10-100 m(0) (m(0) is the rest mass of an electron) and condense into the unconventional (anisotropic) superconducting state. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3683408]