Neutron scattering experiments have revealed a fascinating interplay between the hole doping, the spin fluctuations, and the superconductivity of the cuprate superconductors, Recently, electrochemical techniques have been used to produce large single crystals of La2CuO4+y, which has mobile oxygen dopants, Staging behavior of the excess oxygen has been demonstrated, and the low-energy spin fluctuations in stage 6 La2CuO4+y have been measured. The spin fluctuations are incommensurate with the lattice and have spatial, energy, and temperature dependencies very much like those in La2-xSrxCuO4, with similar high transition temperature. This establishes the universality of the incommensurate spin fluctuations among the La2CuO4-based superconductors.