As the basic formula in fluid mechanics,the numerical solution of the Reynolds equation has always been one of the important research directions in the field of fluid lubrication.Based on the basic form of Reynolds equation,the process of solving the Reynolds equation by finite differential method,finite element method and finite volume method were introduced separately,and the characteristics and problems of each method were discussed.The application of multigrid method combined with the above methods in solving Reynolds equation was introduced,it was pointed out that the multigrid method has made a great breakthrough in the efficiency of solving Reynolds equation,but it has not significantly improved the accuracy of solution.The application of isogeometric analysis(IGA) method in solving Reynolds equation was introduced,it was pointed out that the IGA method has high efficiency and accuracy in solving Reynolds equation,but there are still some problems such as the ininterpolation of the spline function and the generality of the IGA in the solution of the Reynolds equation.The research direction of IGA in solving Reynolds equation was put forward,such as introducing a suitable spline representation for a specific Reynolds equation,introducing a new boundary condition loading mode through modifying the discrete mode of IGA theory and Reynolds equation,etc.As there is still no stable and applicable method on the problem of complex solving domain and boundary treatment when solving Reynolds equation,it was suggested to combine IGA method and multigrid method to solve Reynolds equation,so as to further improve the efficiency and accuracy of solution