In this paper we discuss theoretical modelling methods for the design of photonic crystal and photonic quasi-crystal (PQC) LEDs - and apply them to the analysis of the extraction enhancement performance and shaping of the emitted beam profile of PQC-LED structures. In particular we investigate the effect of the pitch of the PQC patterning, and consider the physical mechanisms giving rise to performance improvements. In addition, we examine the relative contributions to performance improvements from effective index reduction effects that alter the conditions for total internal reflection at the device air interface, and from photonic crystal scattering effects that give rise to radically improved extraction performance. Comparisons are made with the performance of recently fabricated devices.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.