We are progressively approaching the physical limits of microcavity LEDs (MC-LEDs) for high brightness, high efficiency LEDs. They are promising high efficiency devices and they offer the very attractive prospect of full planar fabrication process. However, to compete with other high efficiency LED schemes, they need to approach or surpass the 50 % efficiency mark. We first explore the limits of planar MC-LEDs in both the GaAllnAsP and GaInAlN materials systems, and show that the single-step extraction limit is in the 40 % range at best, depending on the materials system used, with the largest part of the non-extracted light being emitted into guided modes. The waveguided light can itself be extracted by photon recycling, when the internal quantum efficiency is high. Otherwise, another extraction scheme for that light is provided by various photonic-crystal-assisted extraction schemes. Simple photonic crystals (PCs) appear to lack the omnidirectional extraction properties required. However, more rotation-invariant PCs like Archimedean tilings allow to obtain such extraction with added efficiencies already in the 10% range. We discuss the further improvements to such structures.