We present the recent advances in Cc-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 CeRh2Si2, Ce2Ni3Ge5, CeIn3, CeRhIn5, and CeIrSi3. For these compounds, the Neel temperature T-N decreases with increasing pressure and reaches zero at the quantum critical pressure Pc. Superconductivity appears around P-c. In CeRu2, CeCoIn5, and CePt3Si, 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 Pc.