The recent developments in the study of Bose-Einstein condensation of neutral atoms are described. These studies aim to observe this phenomenon in a Bose gas where the quantum statistics of the particles, rather than the interactions between them, dominate the transition. The latest techniques use a combination of laser and evaporative cooling to get to the very low temperatures, in the nanokelvin regime, that are required to see condensation. In recent experiments at the Joint Institute for Laboratory Astrophysics of the University Colorado and the National Institute of Standards and Technology, Bose-condensed assemblies of rubidium atoms have been produced and their properties investigated. The relationship of this work to other phenomena in condensed matter and quantum field theory is discussed.