Electron probe microanalysis (EPMA) is an in-situ and non-destructive analytical technique with high spatial resolution and an increasingly important analysis tool in materials science and geosciences. This study summarizes the principles and functions of EPMA, and the problems and difficulties, along with the recent advances in quantitative analysis of EPMA. A routine EPMA procedure includes preparing samples, setting analytical conditions, acquiring data, and evaluating results. Caution is required in all steps to obtain high-quality analytical results. The problems and difficulties commonly encountered in EPMA are discussed and the corresponding measures and solutions required to resolve them are proposed. Specific analytical methods are suggested to make accurate analysis of some specific minerals. We also summarized the challenges and solutions in light element analysis, trace element analysis, EPMA U-Th-Pb total dating, combined analysis with wavelength-and energy-dispersive X-ray spectroscopy, submicron spatial resolution analysis at low accelerating voltages, iron oxidation state analysis, and standard reference materials.