Abstract. Contemporary cosmological observations provide strong support for a 'standard model' of general relativistic cosmology whose constituents - radiation, baryons, dark matter and a cosmological constant - have now been measured with unprecedented precision. Understanding the formation of structure in such a universe, however, with tiny initial density fluctuations evolving into a complex Cosmic Web of dark matter, galaxies and gas, continues to be an interesting and challenging problem, despite several decades of progress. The non-linear nature of gravitational instability, combined with the stochastic nature of the initial fluctuations, prevents us from weaving a Cosmic Web using fully analytical methods. In parallel, modelling galaxy formation and evolution is fraught with large uncertainties in the astrophysics of gas across cosmic time. One is therefore prevented from analytically assembling a realistic universe from its constituent parts. In this talk, I will argue that there is, in fact, much to be gained from analytical approximations and statistical models used in concert with numerical simulations of structure formation. I will review the current status of such model building efforts and then focus on several open questions and avenues of current interest in the field. In particular, I will highlight how the connection between galaxy environment and galaxy assembly history (the so-called 'assembly bias') can be a powerful probe of galaxy evolution and cosmology.
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