Using Bethe’s hypothesis, C. N. Yang exactly solved the one-dimensional (1D) delta-function interacting spin-1/2 Fermi gas with an arbitrary spinimbalance in 1967. At that time, using a different method, M. Gaudin solved the problem of interacting fermions for the spin-balanced case. Later, the 1D delta-function interacting fermions problem was named the Yang-Gaudin model. This model signi?cantly lays out a profound legacy of quantum integrability, where particles scatter without di?raction.

　　In this talk, I will briefly review recent theoretical and experimental developments of the Yang-Gaudin model on a variety of quantum many-body phenomena, such as fractional excitations, collective motions of quasiparticles, Gruneisen magnetocaloric effect, spin incoherent liquids, Flde-Ferrell-LarkinOvchinnikov (FFLO)-like pairing correlation, universal thermodynamics, and quantum criticality, showing the essence of quantum many-body physics in both spin and charge degrees of freedom.