We have carried out the electrical resistivity measurements under high pressures up to 24 GPa for CeTX3 (T: Co and Ir, X: Si and Ge), CePd5Al2 and YbIr2Zn20 in order to investigate quantum criticality and superconductivity. Antiferromagnets CeTX3 with the non-centrosymmetric tetragonal structure show superconductivity under high pressures and reveal a huge upper critical field for H parallel to [001]. An antiferromagnet CePd5Al2, which is an isostructural family of a heavy fermion superconductor NpPd5Al2, also shows superconductivity under high pressures. In these compounds, superconductivity appears in the vicinity of quantum critical point. On the other hand, YbIr2Zn20 without magnetic ordering approaches to the quantum critical point with increasing pressure, and exhibits a super-heavy fermion state exceeding 10 J/(K-2 center dot mol).