Abstract: Nowadays the simulation methods for heterogeneous materials and structures are still faced with challenges of complex constitutive modeling and costly multiscale computation, which are expected to be overcome by the emerging data-driven computational homogenization methods. Data-driven computational homogenization method aims to save the labor and time costs for constitutive modeling by means of data science. In the meanwhile, it is able to considerably enhance the online computational efficiency for simulating heterogeneous materials and structures by shifting numerous mesoscopic calculations to the offline stage. Data-driven computational homogenization methods can be roughly summarized into two categories according to the functionals to be solved. The first one is based on energy functional, whose key point is to efficiently capture constitutive relation using artificial intelligence and then obtain the solution in the framework of classical computational mechanics. The other one is based on distance functional, whose specificity lies in directly embedding the material data into mechanical simulations. The extremum of distance functional is used to find the state from the constitutive data set that is closest to satisfying the conservation laws, thus bypassing the step of empirical material modeling. The outline of this paper is organized as follows. At first, the basic procedures for conducting multiscale simulations through above two data-driven computational homogenization methods are briefly recalled. Next, numerical simulations concerning the fiber-reinforced composite structure are conducted by adopting both methods. Based on the obtained results, the influence of the number of data points on the computational efficiency and accuracy is evaluated from both qualitative and quantitative perspectives. Finally, the superiorities and weaknesses of both algorithms for conducting multiscale simulations are discussed in terms of different aspects, such as the algorithm implementation, computational accuracy, computational efficiency and post-processing. The outcomes of this paper are expected to offer theoretical basis for developing techniques to efficiently simulate heterogeneous materials and structures.