Galaxy formation is concerned with the processes that formed a heterogeneous Universe from a homogeneous beginning. It encompasses an enormously rich range of different physical phenomena - from the growth of primordial fluctuations in the early Universe, through the cooling and condensation of gas into molecular clouds and stars, to the formation of supermassive black holes that emit copious radiation as they grow within galactic bulges. Galaxy formation has remained one of the most active research areas in astrophysics for the past 50 years.
Remarkably, the evolution of galaxies appears to be quite different from that of the dark matter. The largest dark matter halos form from the "bottom up" through merging and accretion of smaller systems and most are still assembling at the present day. In contrast, the most massive galaxies in the Universe (the giant ellipticals) formed their stars at early epochs. Galaxy growth then somehow shuts down. This quenching process, a kind of "galaxy death", increasingly affects lower mass systems with time and may soon be the fate of our own Milky Way. Galaxies less massive than the Milky Way actively form stars at all cosmic epochs. In fact, the majority of the stars in galactic disks formed in the last 7-9 billion years.
In spite of significant progress in delineating this basic picture, significant pieces of the puzzle remain to be understood. Gravitational collapse is only one of many processes at work in the formation of a galaxy. Gas dissipation and infall, star formation, heating and ejection of gas by supernova explosions, galaxy merging and associated growth of central black holes are all key processes that remain poorly understood. In this talk, I will highlight how surveys of the gas and the stars in nearby and distant galaxies are shedding light on some of these key processes.