We present the recent advances in Ce-based heavy fermion superconductivity. Heavy fermions are formed by the competition between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect. The application of pressure is useful for controlling the electronic states in antiferromagnets such as CeRh 2 Si 2 , Ce 2 Ni 3 Ge 5 , CeIn 3 , CeRhIn 5 , and CeIrSi 3 . For these compounds, the Néel temperature T N decreases with increasing pressure and reaches zero at the quantum critical pressure P c . Superconductivity appears around P c . In CeRu 2 , CeCoIn 5 , and CePt 3 Si, superconductivity is realized at ambient pressure. For these pressure-induced and ambient-pressure superconductors, we clarified their unconventional characteristics of superconductivity, the close relationship between superconductivity and the dimensionality of the electronic states, and a new aspect of superconductivity in the noncentrosymmetric crystal structure, together with its Fermi surface instability at P c .