GaN three-dimensional columnar core-shell LEDs are considered to be one of the promising candidates for prospective solid state lighting. In comparison to conventional planar layer LEDs, columnar core-shell LEDs have many advantages. For instance, in a columnar GaN coreshell LED structure the InGaN/GaN MQW wraps around the column, therefore the light emitting area can be enormously increased. This is the main driving force behind the intense investigation of nanowire and micro-columnar LEDs. In addition, because of the increased area of the MQW, the internal quantum efficiency may be improved by a reduction of the local carrier density, mitigating the efficiency droop. Besides, due to the reduced influence of thermal and lattice mismatch between the substrate and columns, dislocation-free GaN column arrays can be achieved on large area substrates. The main contribution of the present work is the controlled growth of GaN columns and core-shell LEDs by metal-organic vapor-phase expitaxy. The growth conditions which lead to vertical growth of N-polar and Ga-polar GaN columns are systematically investigated. The causes of the vertical growth are explained by surface processes under appropriate conditions for both polarities. Quantitative discussions of growth kinetics of GaN columns are an important feature in this work. The difficulties and the strategies of the MQW and p-GaN shell growth on high aspect ratio GaN columns are presented in detail.