The diffraction of the finite aperture in the optical imaging system restricts further improvement of the resolution of optical microscopy, which is called the diffraction limit. Since raised by Ernst Abbe in 1873, the problem of diffraction limit has been one of the foci of academic research. In recent years, with the rapid development of related fields such as the development of optoelectronic devices including high energy lasers and high sensitivity detectors and the development of new fluorescent probes, the problem of diffraction limit in optical microscopy ushered in a new opportunity, and super-resolution microscopy (SRM) has made remarkable achievements in the past decade. The basic principles of diffraction limited resolution in both space and frequency domains are reviewed, and on this basis, the mechanisms for the various SRM technologies to circumvent the diffraction limit and improve the resolution are explained in detail. The development trends and research directions of various SRM techniques are also introduced. As a new and important development trend of SRM, correlative super-resolution microscopy and its recent progress are reviewed, including correlative studies on SRM and time-lapse live cell fluorescence microscopy, fluorescence lifetime imaging microscopy, spectrometry and spectroscopy, electron microscopy, atomic force microscopy, etc. The role and significance of various correlative super-resolution microscopy are discussed. The future development of super-resolution microscopy and correlative super-resolution microscopy is also prospected.