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Biomimetic anisotropy is defined as intentionally engineered, nature-inspired directional differences in structure, chemistry, roughness, stiffness, or pore architecture. These directional differences lower transport resistance in one direction relative to the opposite direction, which results in rectified transport. In this review, anisotropy design is synthesized across surfaces, porous materials, and soft systems, with transport considered for droplets, low-surface-tension liquids, particles, and soft objects. Biological inspirations are summarized first, and the design lessons that can be transferred to engineered platforms are then extracted. Key anisotropic architectures are classified next, including ratchets and sawtooth textures, bristle- or setae-like fibrillar arrays, grooves and wedges, asymmetric pores and membranes, chemically patterned surfaces, and hierarchical micro–nano combinations. Practical fabrication methods and material choices are reviewed thereafter, spanning micro- and nanofabrication, additive manufacturing, coatings and surface modification, and responsive soft matter. The field is then organized mechanistically around how anisotropy generates directionality through contact-line pinning asymmetry, curvature-driven capillary pressure bias, compliance and elastocapillary coupling, and active rectification under oscillatory forcing. Finally, these mechanisms are connected to application needs in pump-free microfluidics and sampling, long-distance open transport, environmental water management, and fouling-prone self-cleaning systems. Throughout the review, design-to-function links are emphasized, and open challenges are highlighted, including durability under real fluids and contaminants as well as scalable manufacturing and integration. Full article