Creatures in nature perform a variety of activities through adhesion behavior, including moving flexibly and quickly on inclined and vertical walls and even ceilings. Studying the physical and chemical mechanisms underlying their adhesion behaviors can provide effective templates for applications such as climbing robots, grippers, and medical devices. This review summarizes various major types of adhesion that creatures rely on and their morphological structures that enhance adhesion, in addition to discussing their inspiration regarding the design of bionic adhesion systems. First, different adhesion types adopted by creatures in various natural environments are introduced, and the adhesion mechanisms and their theoretical models are summarized. Subsequently, the convergent evolution exhibited in biological adhesion structures is summarized from three perspectives: size limitation, compliance, and fluid transport. The development of the bionic design process wherein researchers imitate the natural biological adhesion process to create artificial adhesives is then presented regarding three mechanisms: chemical bonding adhesives, fiber arrays, and suckers. Fiber arrays are further divided into dry adhesives and wet adhesives. Finally, the shortcomings of the existing bionic adhesion systems and future trends are summarized.