Gallium-nitride (GaN)-based light-emitting diodes (LEDs) are highly efficient sources for general purpose illumination. Visible light communications (VLC) uses these sources to supplement existing wireless communications by offering a large, licence-free region of optical spectrum. Here, we report on progress in the development of micro-scale GaN LEDs (micro-LEDs), optimized for VLC. These blue-emitting micro-LEDs are shown to have very high electrical-to-optical modulation bandwidths, exceeding 800 MHz. The data transmission capabilities of the micro-LEDs are illustrated by demonstrations using ON-OFF-keying, pulse-amplitude modulation, and orthogonal frequency division multiplexing modulation schemes to transmit data over free space at the rates of 1.7, 3.4, and 5 Gb/s, respectively.