The heterostructure engineering of van der Waals (vdW) material systems enables a new type of 2-dimensional (2D) quantum heterostructure with extremely sharp interfaces. We study quantum transport phenomena in low-dimensional van der Waals (vdW) layered materials and their heterostructures. Several current topics of research include: (1) transport in engineered moiré superlattices at vdW interfaces with an adjustable length scale controlled by twist angles between the layers; (2) dissipationless, superfluid magneto-exciton transport in the magneto-exciton condensate formed in graphene double layers by strong interlayer Coulomb interaction; (3) demonstration of unconventional exchange symmetry by braiding anyons. Coulomb interaction couples fractional quantum Hall quasiparticles across the vdW interfaces to create robust anyonic excitons. To probe their exchange symmetry, we build an interferometer using local gates and perform non-local cross-correlation measurements.