Smart adhesives that can be applied and removed on demand play an important role in modern life and manufacturing. However, current smart adhesives made of elastomers suffer from the long-standing challenges of the adhesion paradox (rapid decrease in adhesion strength on rough surfaces despite adhesive molecular interactions) and the switchability conflict (trade-off between adhesion strength and easy detachment). Here, we report the use of shape-memory polymers (SMPs) to overcome the adhesion paradox and switchability conflict on rough surfaces. Utilizing the rubbery–glassy phase transition in SMPs, we demonstrate, through mechanical testing and mechanics modeling, that the conformal contact in the rubbery state followed by the shape-locking effect in the glassy state results in the so-called rubber-to-glass (R2G) adhesion (defined as making contact in the rubbery state to a certain indentation depth followed by detachment in the glassy state), with extraordinary adhesion strength (>1 MPa) proportional to the true surface area of a rough surface, overcoming the classic adhesion paradox. Furthermore, upon transitioning back to the rubbery state, the SMP adhesives can detach easily due to the shape-memory effect, leading to a simultaneous improvement in adhesion switchability (up to 10 ³ , defined as the ratio of the SMP R2G adhesion to its rubbery-state adhesion) as the surface roughness increases. The working principle and the mechanics model of R2G adhesion provide guidelines for developing stronger and more switchable adhesives adaptable to rough surfaces, thereby enhancing the capabilities of smart adhesives, and impacting various fields such as adhesive grippers and climbing robots.