  The roles of critical valence fluctuations of Ce and Yb are discussed as a
key origin of several anomalies observed in Ce- and Yb-based heavy fermion
systems. Recent development of the theory has revealed that a magnetic field is
an efficient control parameter to induce the critical end point of the
first-order valence transition. Metamagnetism and non-Fermi liquid behavior
caused by this mechanism are discussed by comparing favorably with CeIrIn5,
YbAgCu4, and YbIr2Zn20. The interplay of the magnetic order and valence
fluctuations offers a key concept for understanding Ce- and Yb-based systems.
It is shown that suppression of the magnetic order by enhanced valence
fluctuations gives rise to the coincidence of the magnetic-transition point and
valence-crossover point at absolute zero as a function of pressure or magnetic
field. The interplay is shown to resolve the outstanding puzzle in CeRhIn5 in a
unified way. The broader applicability of this newly clarified mechanism is
discussed by surveying promising materials such as YbAuCu4, beta-YbAlB4, and
YbRh2Si2.
