The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. However, current numerical methods for computing the variable-order fractional Laplacian still remain limited. Compared to its constant-order counterpart, the combination of nonlocality and heterogeneity in variable-order fractional Laplacian introduces significant storage and computational challenges. Consequently, many numerical methods developed for the constant-order fractional Laplacian become ineffective for computing the variable-order cases. In this talk, we introduce two numerical methods for the the variable-order Laplacian as well as their fast implementation. Some application of the variable-order fractional Laplacian in diffusion and wave propagation in heterogeneous media will also be discussed.