With the ever-growing demands of real-world and flourishing development of biomimetics, bioinspired structural adhesives have drawn much attention and ushered in tremendous progress in the past several decades. Those delicate adhesive structures in natural organisms provide inexhaustible inspiration for the design of artificial adhesives, some of which have been extensively applied in biomedicine, underwater manipulation, and wearable devices. However, state-of-the-art bioinspired structural adhesives are still far inferior to their natural counterparts in many aspects, facing several crucial barriers on their way toward large-scale deployment. In this perspective, we first provide an overview of the fundamental adhesion models of biological adhesive structures and their artificial analogs. Then, we summarize the current dilemmas of bioinspired structural adhesives by critically comparing them with natural adhesive structures in terms of mechanical properties, structural precision, anisotropy, and intelligence. In the end, we put forward our outlook on future opportunities and development directions from the perspective of novel adhesion models, materials, processing technologies, and crossover cooperation, hoping to inspire new ideas and stimulate the interest of interdisciplinary scientists.