This paper presents a review of the topic of galaxy formation and evolution, focusing on basic features of galaxies, and how these observables reveal how galaxies and their stars assemble over cosmic time. I give an overview of the observed properties of galaxies in the nearby universe and for those at higher redshifts up to z~10. This includes a discussion of the major processes in which galaxies assemble and how we can now observe these - including the merger history of galaxies, the gas accretion and star formation rates. I show that for the most massive galaxies mergers and accretion are about equally important in the galaxy formation process between z = 1-3, while this likely differs for lower mass systems. I also discuss the mass differential evolution for galaxies, as well as how environment can affect galaxy evolution, although mass is the primary criteria for driving evolution. I also discuss how we are beginning to measure the dark matter content of galaxies at different epochs as measured through kinematics and clustering. Finally, I review how observables of galaxies, and the observed galaxy formation process, compares with predictions from simulations of galaxy formation, finding significant discrepancies in the abundances of massive galaxies and the merger history. I conclude by examining prospects for the future using JWST, Euclid, SKA, and the ELTs in addressing outstanding issues.
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