In the last decade, a succession of deep ground and space-based optical/near-infrared surveys has led to the discovery of hundreds of galaxies at z > 6, allowing the first detailed studies of the properties and abundances of these early galaxies. However, to study of the very brightest (L > 2L*) galaxies at high-redshift is more challenging, due to the rarity of such objects over the typically small field-of-view of Wide Field Camera 3 on HST. Supreme-Cam and Hyper-Suprime-Cam have, and will continue to, revolutionise this field in the optical regime, however to push to z = 7 and above, deep near-infrared data is essential. I will present a summary of our recent work using the 1.7 square degrees of the UltraVISTA and UKIDSS UDS near-infrared data to detect extremely luminous z = 6 and 7 LBGs. This work has provided key constraints on the evolution of the rest-frame UV luminosity function from z = 5 to 7, shown the importance of cosmic variance at the bright-end and hinted at a power-law decline in the number counts of the very brightest galaxies. Our sample of extremely bright galaxies are also ideal candidates for detailed follow-up campaigns, and I will end with recent results from our HST/WFC3 and ALMA programs.