The James Webb Space Telescope (JWST), Atacama Large Millimeter Array (ALMA) and a new generation of other ground-based instruments will soon glimpse the first primitive galaxies in the universe, yielding unprecedented insights into the masses the first stars, the luminosities and spectra of protogalaxies, and the chemical evolution of the early IGM. In the past few years numerical simulations of the formation of the first stars and galaxies have made significant strides, but considerable work remains to be done to put estimates of the primordial IMF and the morphology, brightness, and colors of primeval galaxies on firmer footing. The aim of The First Stars and Galaxies: Challenges in the Next Decade is to congregate leading experts on JWST and ALMA with theorists in early structure formation to forge simulation roadmaps for the next several years.