The sum of turbulent fluxes measured by the eddy-covariance method is often 10%~30% lower than available energy (i.e., the net radiation minus the ground heat flux). This systematic bias in the EC method is called the "EC energy closure problem" and has been one of the biggest challenges in micrometeorology. In the past decades, lots of studies have focused on this problem and have found extensive knowledge about it. In this paper, we introduced the reasons to the EC energy closure problem and systematically summarized the understandings on this problem with a discussion regarding the merits and limitations of possible correction methods. Compared with previous overview studies, our study focused on the methods and progresses on the EC energy closure problem using the Large Eddy Simulation (LES). The existing problem, e.g., the lack of high quality and high spatial density of "surface true fluxes" observations (e.g., matric observations), the failure of fully emulating the EC using the LES and how to mechanistically understand that large eddies affect turbulence structures and lead to non-closure problem, hinder the further understanding of the EC energy closure problem. Thus, in the future, focus should be put on the mechanistic understanding of how large eddies affect the non-closure problem and some dense field observations to obtain the high quality "surface true fluxes".