We develop new analytic methods to accurately describe the formation of cosmic large-scale structure. These methods are based on the path integral formalism and allows one to efficiently address a number of long-standing problems in the field. We describe the non-linear evolution of the baryon acoustic oscillations (BAO) in the distribution of matter. We argue for the need for resummation of large infrared (IR) enhanced contributions from bulk flows. We show how this can be done via a systematic resummation of Feynman diagrams guided by well-defined power counting rules. We formulate IR resummation both in real and redshift spaces. For the latter we develop a new method that maps cosmological correlation functions from real to redshift space and retains their IR finiteness. Our results agree well with the N-body simulation data at the BAO scales. This establishes IR resummation within our approach as a robust and complete procedure and provides a consistent theoretical model for the BAO feature in the statistics of matter and biased tracers in real and redshift spaces. Eventually, we perform a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. We evaluate the PDF in the saddle-point approximation and show how it factorizes into an exponent given by a spherically symmetric saddle-point solution and a prefactor produced by fluctuations. The prefactor splits into a monopole contribution which is evaluated exactly, and a factor corresponding to aspherical fluctuations. The latter is crucial for the consistency of the calculation: neglecting it would make the PDF incompatible with translational invariance. We compute the aspherical prefactor using a combination of analytic and numerical techniques, identify the sensitivity to the short-scale physics and argue that it must be properly renormalized. Finally, we compare our result with N-body simulation data and find an excellent agreement.