In the electronic fluids with broken inversion symmetry and strong spin-orbit coupling, we have investigated various topological quantum phenomena and obtained the following results. In noncentrosymmetric superconductors, we clarified the conditions necessary for bringing about a large spin-triplet component. We have succeeded in synthesizing new topological insulators and found that CuxBi2Se3 is a spin-triplet superconductor. We discovered electric-field-effect induced superconductivity in KTaO3 which cannot be made superconducting by conventional chemical doping method.