Gallium nitride (GaN), as a representative wide-bandgap semiconductor, has attracted extensive attention for next-generation power integrated circuits owing to its high critical electric field, high electron saturation velocity, and excellent thermal stability. This paper presents a systematic review of GaN power integration from a platform-to-application perspective. First, the material and device-level advantages of GaN for high-frequency, high-temperature, and high-power-density operation are analyzed. Then, the fundamental monolithic integration platforms based on lateral GaN high electron mobility transistors (HEMTs) are reviewed, as well as the co-integration of key functional components. On this basis, representative GaN integration routes and switching structures are presented. Furthermore, the design methodologies and performance characteristics of key application modules in monolithic GaN power ICs, including gate drivers, integrated half-bridges, voltage references, undervoltage lockout circuits, over-temperature protection, and over-current protection, are comprehensively summarized. The review indicates that GaN monolithic integration can effectively reduce parasitic effects, shorten critical switching paths, improve switching speed, and enhance system efficiency, power density, and reliability, making it highly promising for electric vehicles, aerospace electronics, data centers, and other demanding applications. Meanwhile, several critical bottlenecks remain, including substrate crosstalk, dynamic on-resistance degradation, thermal management, parasitic coupling, and robustness under extreme operating conditions. This work highlights the core technical challenges and emerging development directions of GaN power integrated circuits.