<p>Surface instability, or wrinkling, in film–substrate structures is a pervasive phenomenon in both biological systems and engineering applications, representing a frontier area in soft matter mechanics. This short review summarizes recent advances in theoretical modeling, numerical simulations, and experimental investigations of wrinkling phenomena. We cover a wide range of systems, from half-space to planar film–substrate structures and more complex curved core–shell configurations. The review details the mechanical mechanisms underlying wrinkling initiation, post-buckling evolution, and pattern transitions under diverse loading conditions, including uniaxial and biaxial compression, growth, and swelling, as well as external fields such as thermal, electric, and magnetic stimuli. We place particular emphasis on emerging systems, including multilayer structures, intelligent materials, and functionally graded materials. Furthermore, we highlight the practical applications of wrinkle analysis in biological tissue morphogenesis, flexible electronics, and the characterization of micro- and nano-scale mechanical properties. Additionally, we emphasize studies that employ the exact theory of nonlinear elasticity, clarifying its advantages and necessity in different scenarios. This review provides a comprehensive overview of the state of the art of this active field and outlines promising directions for future research.</p>