I present a comprehensive review of the evolution of galaxy structure in the Universe from the first galaxies currently observable at ∼ 6 down to galaxies observable in the local Universe. Observed changes in galaxy structures reveal formation processes that only galaxy structural analyses can provide. This pedagogical review provides a detailed discussion of the major methods used to study galaxies morphologically and structurally, including the well-established visual method for morphology; Sérsic fitting to measure galaxy sizes and surface brightness profile shapes; and nonparametric structural methods [such as the concentration (), asymmetry (), clumpiness () (CAS) method and the Gini/M parameters, as well as newer structural indices]. These structural indices measure fundamental properties of galaxies, such as their scale, star-formation rate, and ongoing merger activity. Extensive observational results demonstrate how broad galaxy morphologies and structures change with time up to ∼ 3, from small, compact and peculiar systems in the distant Universe to the formation of the Hubble sequence, dominated by spirals and ellipticals. Structural methods accurately identify galaxies in mergers and allow measurements of the merger history out to ∼ 3. I depict properties and evolution of internal structures of galaxies, such as bulges, disks, bars, and at >1 large star-forming clumps. I describe the structure and morphologies of host galaxies of active galactic nuclei and starbursts/submillimeter galaxies, along with how morphological galaxy quenching occurs. The role of environment in producing structural changes in galaxies over cosmic time is also discussed. Galaxy sizes can also change with time, with measured sizes up to a factor of 2–5 smaller at high redshift at a given stellar mass. I conclude with a discussion of how the evolving trends, in sizes, structures, and morphologies, reveal the formation mechanisms behind galaxies and provides a new and unique way to test theories of galaxy formation.


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