When the governing equations resultant from conservation laws are solved to simulate fluid flow problems， one of key issues is to evaluate numerical fluxes at the cell interface， which is also called flux reconstruction. Since the conservative variables of discrete governing equations are defined at the solution points， how to use the values at the solution points to calculate the flux at the cell interface is one of the most important and challenging issues in computational fluid dynamics （CFD）. In order to resolve this problem， various numerical algorithms have been developed， such as finite difference schemes based on mathematical reconstruction， the Riemannian flux solver based on partial physical reconstruction， and the newly-developed gas kinetic scheme （GKS）， lattice Boltzmann flux solver （LBFS）， gas kinetic flux solver （GKFS） based on the fully physical reconstruction. In this paper， several typical flux reconstruction methods are reviewed and analyzed. In particular， the research progress of LBFS and GKFS and their applications are introduced. Finally， some challenges and possible research directions of LBFS and GKFS are addressed.