Many biological materials utilize hierarchical surface structures to achieve their wetting-based functions, e.g. self-cleaning and antifogging. In this paper, a classification method is proposed for both biological and artificial materials with hierarchical surface structures to establish the functional map of various hierarchical surface structures. From the viewpoint of geometric features, the constituent building elements on functional surfaces are categorized into dimensional classes both at the micrometer and nanometer scales. Following this classification, one can correlate the biological functions, especially those related to superhydrophobicity, with surface morphologies. In addition to natural biological tissues, we also briefly review the fabrication techniques for realizing these superhydrophobic structures in the laboratory. This dimensionality classification may serve as a guide for future analysis, design and preparation of surfaces with tuned functions achieved by geometrical morphologies.