Finding the exotic phenomena in strongly correlated electron systems (SCESs) and understanding the corresponding microphysics have long been the research frontiers of condensed matter physics. The remarkable examples for the intriguing phenomena discovered in past years include unconventional superconductivity, heavy Fermion behaviors, giant magneto-resistance and so on. A fascinating type of rare earth hexaboride RB6 (R = Sm, Yb, Eu and Ce) belongs to a strongly correlated electron system (SCES), but shows unusual ambient-pressure and high-pressure behaviors beyond the phenomena mentioned above. Particularly, the recent discovery of the coexistence of an unusual metallic surface state and an insulating bulk state in SmB6, known to be a Kondo insulator decades ago, by theoretical calculations and many experimental measurements creates new interest for the investigation of the RB6. This significant progress encourages people to revisit the RB6 with an attempt to establish a new physics that links the SCES and the unusual metallic surface state which is a common feature of a topological insulator (TI). It is well known that pressure has the capability of tuning the electronic structure and modifying the ground state of solids, or even inducing a quantum phase transition which is one of the kernel issues in studies of SCESs. In this brief review, we will describe the progress in high pressure studies on the RB6 based on our knowledge and research interests, mainly focusing on the pressure-induced phenomena in YbB6 and SmB6, especially on the quantum phase transitions and their connections with the valence state of the rare earth ions. Moreover, some related high-pressure results obtained from CeB6 and EuB6 are also included. Finally, a summary is given in the conclusions and perspectives section.