Auxiliary nanostructures introduce additional flexibility into optomechanical manipulation schemes. Metamaterials and metasurfaces capable to control electromagnetic interactions at the near-field regions are especially beneficial for achieving improved spatial localization of particles, reducing laser powers required for trapping, and for tailoring directivity of optical forces. Here, optical forces acting on small particles situated next to anisotropic substrates, are investigated. A special class of hyperbolic metasurfaces is considered in details and is shown to be beneficial for achieving strong optical pulling forces in a broad spectral range. Spectral decomposition of Green’s functions enables identifying contributions of different i...