Organic electrochemical transistors rely on ionic-electronic volumetric interaction to provide a seamless interface between biology and electronics with outstanding signal amplification. Despite their huge potential, further progress is limited owing to the lack of understanding of the device fundamentals. Here, we investigate organic electrochemical transistors in a wide range of experimental conditions by combining electrical analyses and device modeling. We show that the measurements can be quantitatively explained by nanoscale ionic-electronic charge interaction, giving rise to ion buffering and interface charge compensation. The investigation systematically explains and unifies a wide range of experiments, providing the rationale for the development of high-performance electronics. Unipolar inverters - universal building blocks for electronics - with gain larger than 100 are demonstrated. This is the highest gain ever reported, enabling the design of devices and circuits with enhanced performance and opening opportunities for the next-generation integrated bioelectronics and neuromorphic computing.