The epoch of galaxy assembly from 2 z 4 marks a critical stage during the evolution of today's galaxy population. During this period, the star-formation activity in the Universe was at its peak level, and the structural patterns observed among galaxies in the local Universe were not yet in place. A variety of novel techniques have been employed over the past decade to assemble multiwavelength observations of galaxies during this important epoch. In this primarily observational review, I present a census of the methods used to find distant galaxies and the empirical constraints on their multiwavelength luminosities and colors. I then discuss what is known about the stellar content and past histories of star formation in high-redshift galaxies; their interstellar contents including dust, gas, and heavy elements; and their structural and dynamical properties. I conclude by considering some of the most pressing and open questions regarding the physics of high-redshift galaxies, which are to be addressed with future facilities.