As a typical strong coupling,highly nonlinear and multi-variable dynamic system,power system has complex nonlinear dynamics behaviors. Its nonlinear physical characteristic is one of the important causes of low frequency oscillation( LFO). Basing on bifurcation and chaos theory,this paper summarizes the research achievements of LFO nonlinear mechanism,including the discovery and mechanism of nonlinear singular phenomena,nonlinear mechanism of promoting a small single-generator system to large multi-generator system,searching methods of bifurcation and chaos attractor,controlling of bifurcation and chaos parameters,etc. Considering the requirements of grid safe operation,five problems of nonlinear LFO are proposed,such as identification of LFO triggering mechanism,oscillation patterns recognition and so on. This paper aims to provide guidence in researching low frequency oscillation of power system in field of nonlinear dynamics.