Abstract: Ultra-low frequency oscillations (ULFOs) have occurred many times in modern power systems, threatening the safe and stable operation of the power grid. In this paper, according to the corresponding mathematical model and the characteristics of the oscillation trajectory, the classification of four mathematical mechanisms of the ULFO was analyzed and summarized, that is, negative damping oscillation, forced oscillation, switching-type oscillation and other complex oscillations; and the corresponding bifurcation characteristics were given from the perspective of parameter change. Furthermore, based on the above mechanism classification, respectively summarized the corresponding analysis methods. Next, from the three aspects of improving unit damping, improving system damping and adjusting system structure, analyzed the research status of ULFO suppression. Finally, aiming at the switching-type ULFO which were rarely studied at present, the possible future research contents and directions were discussed from the perspectives of analytical models, analytical methods, dynamic mechanisms, physical characteristics, suppression methods, and practical verification.