The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of electronic nematicity, which is characterized by rotational symmetry breaking, may also promote high-temperature superconductivity. FeSe-based superconductors are suitable to study this issue [1], because FeSe exhibits a nonmagnetic nematic order that can be suppressed by S or Te substitution for Se. I will review recent studies of FeSe-based superconductors, which show quite exotic superconducting states. In FeSe1-xSx superconductors, the nematic order can be completely suppressed at x=0.17, above which the superconducting properties change drastically with a significantly reduced critical temperature Tc *2,3+. From recent muon spin rotation (μSR) measurements *4], we find evidence for a novel ultranodal pair state with broken time reversal symmetry [5]. In the Te substitution case, however, we find quite different behavior; the suppression of nematic order leads to an enhancement of Tc, which is likely associated with quantum critical fluctuations of nematicity [6].