The amazing adhesion of gecko pads to almost any kind of surfaces has inspired a very active research direction over the last decade: the investigation of how geckos achieve this feat and how this knowledge can be turned into new strategies to reversibly join surfaces. This article reviews the fabrication approaches used so far for the creation of micro- and nanostructured fibrillar surfaces with adhesive properties. In the light of the pertinent contact mechanics, the adhesive properties are presented and discussed. The decisive design parameters are fiber radius and aspect ratio, tilt angle, hierarchical arrangement and the effect of the backing layer. Also first responsive systems that allow thermal switching between nonadhesive and adhesive states are described. These structures show a high potential of application, providing the remaining issues of robustness, reliability, and large-area manufacture can be solved.