  Heavy fermions have served as prototype examples of strongly-correlated
electron systems. The occurrence of unconventional superconductivity in close
proximity to the electronic instabilities associated with various degrees of
freedom points to an intricate relationship between superconductivity and other
electronic states, which is unique but also shares some common features with
high temperature superconductivity. The magnetic order in heavy fermion
compounds can be continuously suppressed by tuning external parameters to a
quantum critical point, and the role of quantum criticality in determining the
properties of heavy fermion systems is an important unresolved issue. Here we
review the recent progress of studies on Ce based heavy fermion
superconductors, with an emphasis on the superconductivity emerging on the edge
of magnetic and charge instabilities as well as the quantum phase transitions
which occur by tuning different parameters, such as pressure, magnetic field
and doping. We discuss systems where multiple quantum critical points occur and
whether they can be classified in a unified manner, in particular in terms of
the evolution of the Fermi surface topology.
