Abstract: A quantum critical point (QCP) is a continuous ground state transformation at T=0, tuned by an external parameter such as pressure, chemical doping or magnetic field. The critical behavior associated with this T=0 thermodynamic singularity may be the common feature underlying the similar phase diagrams found in a wide variety of strongly correlated systems, including cuprates, ruthenates, heavy fermions and iron pnictides. Among these systems, the heavy fermion compounds, rare-earth materials exhibiting large effective masses, have played a particularly important role for investigating the evolution of the Fermi surface across a QCP. In these materials it is the competing tendency of conduction electrons to screen or to mediate a magnetic coupling among the f-electrons that ultimately leads to a QCP. The important and still open question regarding the underlying mechanism of the QCP is whether the Fermi surface volume changes abruptly at the onset of magnetic ordering. Following a broad introduction, I will focus on two heavy fermion superconductors: CeMIn5 with M=Co,Ir. These recently discovered compounds illustrate well the shortcomings of our current understanding of quantum criticality: despite the thermodynamic and transport evidence for non-Fermi Liquid behavior in these systems, their Fermi surface, as investigated by de Haas van Alphen effect, does not show a drastic change across the putative QCP. The implications and possible scenarios will be discussed.