Computer simulations and theoretical understanding have now reached a stage where simulations are increasingly able to tackle the complexity of galaxy formation and evolution. This talk will describe in particular the successes and challenges of high-resolution hydrodynamic galaxy simulations, now including radiative pressure feedback, in trying to understand the Hubble Space Telescope observations of galaxies during the period of most vigorous star formation (1 < z < 3, "Cosmic High Noon”). The lower stellar mass star-forming galaxies at z > 1 have recently been shown to have mostly elongated (prolate) stellar distributions rather than disks or spheroids, and our simulations may explain why. A large fraction of star-forming galaxies at redshifts 1 < z < 3 are found to have massive stellar clumps; these originate from violent disk instabilities in our simulations, which also play a role in galaxy compaction and help to create compact galactic spheroids ("nuggets"). We are following in our simulations how angular momentum evolves as gas falls toward the inner galaxy and becomes stars. The talk will also describe the Assembling Galaxies of Resolved Anatomy (AGORA) program to run high-resolution simulations using as much as possible the same initial conditions, physical assumptions, and output analysis procedures. AGORA will systematically compare galaxy simulations using a wide variety of computer codes with each other and with observations, and thus improve understanding of galaxy formation.