We clarify that metamagnetic transitions in three dimensions show unusual properties as quantum phase transitions if they are accompanied by changes in Fermi-surface topology. An unconventional universality deeply affected by the topological nature of Lifshitz-type transitions emerges around the marginal quantum critical point (MQCP). Here, the MQCP is defined by the meeting point of the finite temperature critical line and a quantum critical line running on the zero temperature plane. The MQCP offers a marked contrast with the Ising universality and the gas-liquid-type criticality satisfied for conventional metamagnetic transitions. At the MQCP, the inverse magnetic susceptibility À1 has a diverging slope as a function of the magnetization m (namely, jd À1 =dmj ! 1) in one side of the transition, which should not occur in any conventional quantum critical phenomena. The exponent of the divergence can be estimated even at finite temperatures. We propose that such an unconventional universality indeed accounts for the metamagnetic transition in ZrZn 2 .Itinerant ferromagnets such as ZrZn 2 , 1,2) UGe 2 , 3) and nearly ferromagnetic metals such as Sr 3 Ru 2 O 7 4) show metamagnetic transitions. The magnetizations show jumps at magnetic fields separating the low-field phase with a smaller magnetic moment from the high-field phase with a higher moment. The first-order transition characterized by the magnetization jump terminates at a finite-temperature critical point. The universality around the critical point is regarded as the Ising type, which is equivalent to the gasliquid critical points. The critical temperature can, however, be controlled to zero, for example, by pressure, which offers a field of quantum critical phenomena. The metamagnetic transition and its quantum critical point (QCP) in itinerant electron systems have attracted interest because of its intriguing nature of fluctuations leading to possible nonFermi-liquid behavior as well as superconductivity found in UGe 2 near the metamagnetic transition. 5) A simple scope of the QCP is offered by the suppressions of critical temperatures of gas-liquid (or equivalently Ising) transitions, T c , by quantum fluctuations. 6) The QCP of magnetic transitions in itinerant electron systems has been analyzed by the same framework of the suppressed symmetry breaking by the quantum fluctuations, 7-9) which is expressed essentially by the d þ z dimensional Ising criticality with the spatial dimensionality d being added by the dynamical exponent z representing the quantum dynamics. The quantum criticality of the metamagnetic transition has been interpreted so far by the same conventional QCP of the Ising type. 10) Recently, however, for two-dimensional systems, a completely different type of quantum critical phenomena has been proposed for metal-insulator transitions 11,12) as well as for the Lifshitz transition, 13) where the topological nature of the transition deeply modifies the above conventional picture. In this case, the phase diagram is qualitatively different...