Increasing optical power and electrical-to-optical conversion efficiency enable visible light-emitting diodes to advance into new applications and wider markets. InGaAlP/GaAs and InGaN/sapphire material systems cover the whole visible spectrum of saturated colors used for display, signage, and automotive use. A combination of blue InCaN LEDs with phosphor delivers a "white" spectrum adequate for most lighting needs. Demand for high optical power requires larger chips suitable for high-current operation. Current crowding effects and their negative consequences for chip performance and reliability limit the performance of high-power chips based on both material systems. Despite the differences between InGaAlP/GaAs and InGaN/sapphire chip structures, a number of common design concepts leading to higher external efficiency and total luminous output have been proposed, including large chips operating at high drive currents. This paper highlights fundamental current spreading and reliability issues related to the chip size and operating current density, outlines a framework for quantitative analysis, proposes and compares a number of novel high-power chip designs.