Light-emitting diodes (LEDs) based on Gallium Nitride (GaN) have been revolutionizing various applications in lighting, displays, biotechnology, and other fields. However, their energy efficiency is still below expectations in many cases. An unprecedented diversity of theoretical models has been developed for efficiency analysis and GaN-LED design optimization, including carrier transport models, quantum well recombination models, and light extraction models. This invited review paper provides an overview of the modeling landscape and pays special attention to the influence of III-nitride material properties. It thereby identifies some key challenges and directions for future improvements.