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The ability to actuate liquids remains a fundamental challenge in smart microsystems, such as those for soft robotics, where devices often need to conform to either natural or three-dimensional solid shapes, in various orientations. Here we propose a hierarchical nanotexturing of piezoelectric films as active microfluidic actuators, exploiting a unique combination of both topographical and chemical properties on flexible surfaces, whilst also introducing design concepts of shear hydrophobicity and tensile hydrophilicity. In doing so, we create nanostructured surfaces that are, at the same time, both slippery (low in-plane pinning) and sticky (high normal-to-plane liquid adhesion). By enabling fluid transportation on such arbitrarily shaped surfaces, we demonstrate efficient fluid motions on inclined, vertical, inverted, or even flexible geometries in three dimensions. Such surfaces can also be deformed and then reformed into their original shapes, thereby paving the way for advanced microfluidic applications.