The inner core of a typhoon plays a crucial role in storm intensification and is especially critical for rapid increases in storm intensity. Most of the energy exchange occurs in the inner core, including the eyewall. Moist air rising from the warm ocean releases latent heat, increasing wind speeds and sustaining the warm-core structure through secondary circulations. A deeper understanding of the physical processes in the inner core is essential for improving intensity forecasts and disaster preparedness and mitigation. This paper reviews key studies on the inner core. We focus on lead–lag relationships, eyewall replacement cycles, and waves and oscillations, which are topics that can greatly enhance forecasting capabilities. We highlight limitations of current research and propose key scientific questions that would provide essential insights to improve forecasts and support disaster reduction strategies. These include: (1) what are the physical processes that drive the lead–lag relationship between eyewall convection and intensity changes, and how does the time lag vary across typhoons? (2) What conditions favor merging of the inner and outer eyewalls and completion of the eyewall replacement cycle, potentially leading to rapid intensification before landfall? (3) How do waves and oscillations in the eyewall influence typhoon intensity variations?