Surface wrinkles driven by elastic instabilities have attracted significant interest in the field of materials science and engineering. They are simple and readily fabricated with various patterns of tunable size, morphology and surface topography from a wide range of material systems. Recently, they have been investigated as a new type of dry adhesives. In this review, after a brief introduction of different methods to prepare wrinkle surfaces, we focus on the investigation of dry adhesion mechanisms in different material systems. By exploiting wrinkle dimension, morphology, modulus, curvature, and different contacting surfaces (flat, hemispherical, spherical) and their complementarity, we show adhesion enhancement, reduction and selectivity. By comparing experimental results with theoretical predictions, we aim to provide a guideline to design and engineer wrinkle-based dry adhesives. Several examples of applications of engineered wrinkles are also demonstrated, including pick, release and transfer of nanoparticles and bulk materials, and gecko-like hybrid adhesives. The review is concluded with perspectives on the wrinkling technology for smart dry adhesives.