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We propose metasurface holograms as a novel platform to generate optical trap arrays for cold atoms with high fidelity, efficiency, and thermal stability. We developed design and fabrication methodologies to create dielectric, phase-only metasurface holograms based on titanium dioxide. We experimentally demonstrated optical trap arrays of various geometries, including periodic and aperiodic configurations with dimensions ranging from 1D to 3D and the number of trap sites up to a few hundred. We characterized the performance of the holographic metasurfaces in terms of the positioning accuracy, size and intensity uniformity of the generated traps, and power handling capability of the dielectric metasurfaces. Our proposed platform has great potential for enabling fundamental studies of quantum many-body physics, and quantum simulation and computation tasks. The compact form factor, passive nature, good power handling capability, and scalability of generating high-quality, large-scale arrays also make the metasurface platform uniquely suitable for realizing field-deployable devices and systems based on cold atoms.