Super-resolution fluorescence microscopy has always been a hot research field. The emergence of various super-resolution fluorescence imaging techniques has broken the optical diffraction limit and improved the spatial resolution to nanoscale. However, for higher requirements on temporal and spatial resolution, the current super-resolution fluorescence microscopes still face two problems of the triangular constraint relation of spatial resolution, temporal resolution and field of view, and low detection sensitivity. However, with the recent development of the new imaging mechanism based on quantum correlation, the super-resolution fluorescence microscopes based on fluorescence quantum property and quantum correlation imaging have been developed. The introduction of new imaging modes and new physical quantities not only increases the amount of information but also improves the efficiency of image information acquisition. A new research route for the development of super-resolution fluorescence microscopy is provide. This review introduces the technological principle, advantages and disadvantages of the current super-resolution fluorescence microscopes as well as the main technical problems faced by them. Some new super-resolution fluorescence microscopes based on quantum correlation are introduced and the future development direction of super-resolution fluorescence microscopy is discussed. It is expected that this review can provide some references for the researches in this field.