Two-dimensional (2D) materials(1,2) and the associated van der Waals (vdW) heterostructures(3-7) have provided great flexibility for integrating distinct atomic layers beyond the traditional limits of lattice-matching requirements, through layer-by-layer mechanical restacking or sequential synthesis. However, the 2D vdW heterostructures explored so far have been usually limited to relatively simple heterostructures with a small number of blocks(8-18). The preparation of high-order vdW superlattices with larger number of alternating units is exponentially more difficult, owing to the limited yield and material damage associated with each sequential restacking or synthesis step(8-29). Here we report a straightforward approach to realizing high-order vdW superlattices by rolling up vdW heterostructures. We show that a capillary-force-driven rolling-up process can be used to delaminate synthetic SnS2/WSe2 vdW heterostructures from the growth substrate and produce SnS2/WSe2 roll-ups with alternating monolayers of WSe2 and SnS2, thus forming high-order SnS2/WSe2 vdW superlattices. The formation of these superlattices modulates the electronic band structure and the dimensionality, resulting in a transition of the transport characteristics from semiconducting to metallic, from 2D to one-dimensional (1D), with an angle-dependent linear magnetoresistance. This strategy can be extended to create diverse 2D/2D vdW superlattices, more complex 2D/2D/2D vdW superlattices, and beyond-2D materials, including three-dimensional (3D) thin-film materials and 1D nanowires, to generate mixed-dimensional vdW superlattices, such as 3D/2D, 3D/2D/2D, 1D/2D and 1D/3D/2D vdW superlattices. This study demonstrates a general approach to producing high-order vdW superlattices with widely variable material compositions, dimensions, chirality and topology, and defines a rich material platform for both fundamental studies and technological applications.