I discuss the discovery of a population of extremely luminous, but very dusty and very distant, galaxies in the submillimetre (submm) waveband. Almost all the light emitted by the stars in these galaxies is absorbed by interstellar dust (which is produced by the same stars) and re-radiated in the far-infrared. This leaves little to be detected at optical wavelengths and results in most of these galaxies being effectively invisible in even the deepest optical images obtainable with the Hubble space telescope. Yet this population contributes most of the light emitted by galaxies at wavelengths of lambda > or approximately equal 100 microm over the lifetime of the Universe. Together with other observations, this suggests that perhaps up to half of all the stars seen in galaxies today were formed in very dusty regions in the early Universe. Hence, studying the galaxies detected in the submm wavebands is critical for developing and testing models of galaxy formation and evolution. Individually, these luminous submm galaxies are forming stars a thousand times faster than our Galaxy is at the present-day, sufficiently fast to form all the stars in the most luminous galaxy in the local Universe within a short period, up to ca. 0.1-1 Gyr. Detailed study of a handful of examples of this population confirm these estimates and unequivocally identify the bulk of this submm-selected population with dusty, star-burst galaxies in the very distant Universe. The extreme faintness of this population in the optical and near-infrared wavebands, resulting from their obscuration by dust, means that our understanding of the detailed nature of these galaxies is only slowly growing. I give a brief summary of the properties of these highly obscured systems and describe the wide range of facilities currently being developed that will greatly aid in their study.