Ideally, cosmological surveys should be analyzed in terms of the joint constraints they place on the initial conditions from which structure originates and on their subsequent gravitational evolution. In this talk, I will describe an innovative statistical data analysis approach designed for the ab initio simultaneous analysis of the formation history and morphology of the large-scale structure of the inhomogeneous Universe. As three-dimensional large-scale structure surveys contain a wealth of information that cannot be trivially extracted due to the non-linear dynamical evolution of the density field, I will discuss methods designed to improve upon previous techniques by including non-Gaussian and non-linear data models for the description of late-time structure formation.Through the talk, I will demonstrate the application of our inference framework to the Sloan Digital Sky Survey data release 7 and describe the primordial and late-time large-scale structure in the Sloan volume. I will show how the approach has led to the first quantitative reconstructions of the cosmological initial conditions from galaxies, an exceptionally detailed characterization of the dynamic cosmic web underlying the observed galaxy distribution, and a new, enhanced catalog of cosmic voids probed at the level of the dark matter distribution, deeper than with the galaxies. Finally, I will present research plans aimed at further physical investigations using cosmological reconstructions.