The research actuality of the bifurcation and chaos phenomena in the H-bridge converter is summarized. Two discrete models of the typical H-bridge converter are introduced in detail, and their applicability is also analyzed and assessed. The existing stability analysis approaches and the numerical simulation methods used in the nonlinear study of H-bridge converter are analyzed concretely, and the merits and demerits are also summarized. With the method of Lyapunov exponent, those two discrete models are verified, and the difference between them, which are changeable according to the switching frequency, is analyzed and explained in detail. The application of time-delayed feedback control(TDFC）method and extended time-delayed feedback control method(ETDFC), which are used to control the chaos in H-bridge converter, is introduced, and their superiorities and deficiencies are evaluated. Finally, several future researches on the bifurcation and chaos phenomena of H-bridge converter are proposed, which provides some instructions for follow-up study.