Nature has developed reversibly adhesive surfaces whose stickiness has attracted much research attention over the last decade. The central lesson from nature is that "patterned" or "fibrillar" surfaces can produce higher adhesion forces to flat and rough substrates than smooth surfaces. This paper critically examines the principles behind fibrillar adhesion from a contact mechanics perspective, where much progress has been made in recent years. The benefits derived from "contact splitting" into fibrils are separated into extrinsic/intrinsic contributions from fibril deformation, adaptability to rough surfaces, size effects due to surface-to-volume ratio, uniformity of stress distribution, and defectcontrolled adhesion. Another section covers essential considerations for reliable and reproducible adhesion testing, where better standardization is still required. It is argued that, in view of the large number of parameters, a thorough understanding of adhesion effects is required to enable the fabrication of reliable adhesive surfaces based on biological examples.