Abstract: Heavy-Fermion system is a prototype of strongly correlated electron systems，which displays a rich degree of ground states due to the coexisting and competing interactions such as Coulomb and magnetic interactions. Meanwhile，different ground states can be tuned back and forth with controlling parameters such as pressure，doping and magnetic field. In this article，general behaviors of heavy-Fermion systems under pressure are discussed and the researches on superconductivity and quantum critical phenomena are of the focus，which have deepened our understanding on the strongly-correlated electron systems. Interesting results on the so called 115 family are taken as an example to demonstrate how superconductivity emerges in a textured form with the coexisting antiferromagnetic order and how to apply different spectroscopic methods (field-rotational heat capacity，soft point-contact spectroscopy…) to investigate heavy-Fermion systems under pressure，especially the superconducting order parameter.