Abstract: As the most effective and powerful nonparametric density estimation technique,Kernel Density Estimation（KDE） has been widely analyzed.However,the practical use of KDE is not widespread because of high computational complexity due to the intensive use of the available data.In order to surmount this computational difficulty,researchers have proposed several schemes from different points of view.In this paper,after the brief introduction of conventional KDE,we analyze a few classes of fast KDE algorithms for the sake of further advance.