The recent advances of sample fabrications and characterization techniques in low-dimensional van der Waals (vdW) materials have enabled the discoveries of many fascinating physics in vdW materials and their heterostructures and unprecedented control over their optical, electrical and magnetic properties. This session focuses on a series of experimental reports and theoretical proposals of new physical phenomena recently discovered in one-dimensional (1D) and two-dimensional (2D) vdW materials and their heterostructures. Research topics include (not limited to) strongly-correlated physics, moiré superlattices, light-matter interactions in near- and far-fields, advances in material fabrications, and Luttinger liquid physics.