III-nitride micro-pixellated light-emitting diodes (micro-LEDs) are a novel format of light source capable of generating micro-scale, spatially and temporally-controllable light patterns. These devices consist of arrays of LED pixels with diameters in the range of 1 μm to 100 μm and emit light across the ultraviolet-blue-green-red part of the spectrum. In addition, compared with conventional broad-area LED devices, micro-LEDs show improved device performance in many aspects, such as high output power densities and the capability to withstand high injection current densities. For these reasons, micro-LEDs allow the study of interesting LED properties in regimes not accessible to conventional broad-area LEDs and also a wide range of novel LED applications. The research work presented in this thesis focuses on the novel applications of micro-LEDs in visible light communications (VLC) and micro-displays. Due to a reduced current crowding effect and superior thermal management capabilities, micro-LEDs can be driven at very high current densities, resulting in high modulation bandwidths of the devices. For this reason, optical data transmission was demonstrated from individual micro-LED pixels at bit rates of up to 1 Gbit/s using a high-speed probe under a binary amplitude modulation scheme. To make a more practical VLC system, micro-LED devices were integrated with specifically-designed complementary metaloxide-semiconductor (CMOS) electronics, which allow individual micro-LED pixels to be conveniently controlled via a simple computer interface. Such CMOS-controlled micro-LED devices have been demonstrated for data transmission at bit rates of up to 512 Mbit/s by modulating a single CMOS/micro-LED pixel and 1.5 Gbit/s by modulating four CMOS/micro-LED pixels simultaneously. Apart from the application in VLC, CMOS-controlled micro-LED devices can also be used to implement micro-display systems. A colour-tunable micro-display system capable of delivering high-resolution microscale dynamic images and tuning its colour from red to green has been demonstrated based on new LED epitaxial LED structures, micro-LED fabrication, and the CMOS technology. Other work reported in this thesis includes using micro-LEDs for data transmission in plastic optical fibre and investigating the modulation characteristics of colour-converters such as colloidal quantum dots and light-emitting polymer. A detailed study on size-dependent capacitance in III-nitride micro-LEDs, especially the negative capacitance (NC) effect, has also been reported in this thesis. This capacitance research sheds light on the mechanisms underlying the NC effect and is potentially useful for improving the LED performance for VLC and other applications.