The history of the Universe is a story of structure formation: fluctuations in the post-inflation density field collapse to form a ``cosmic web" of dark matter halos, and observations of this large-scale structure offer constraints on cosmological parameters. This thesis presents two studies of large-scale structure probes of cosmology. We first study the distribution of structure as a probe of expansion history. The two-point matter correlation function (2PCF), which counts pairs of dark matter halos separated by a given distance, and its Fourier transform the power spectrum both show the signature of baryons in the early Universe. The baryon acoustic oscillation (BAO) feature represents a fixed distance scale, or standard ruler, which expands with the scale factor and thus constrains expansion history and dark energy. The 2PCF constrains the BAO scale to 1\% precision in modern galaxy surveys, but higher-point statistics like the three-point correlation function and its Fourier transform the bispectrum also carry BAO information. We present a new technique to strategically select the bispectrum triangles most sensitive to BAO. A small number of bispectrum measurements can improve BAO precision by around 15\%, equivalent to lengthening a survey by 30\%. To understand why some bispectrum triangles are more sensitive to BAO than others, we study the structure of BAO in the bispectrum in detail. We then turn to the internal structure of dark matter halos and the evolution of their profiles. The spherically-averaged density of a halo is well described by the Navarro-Frenk-White (NFW) profile, a function of two parameters: concentration, which describes the density of the inner regions of the halo, and halo mass. These two parameters are correlated: the concentration-mass ($c-M$) relation, which predicts concentration as a function of halo mass, has negative slope at low redshifts. We measure the concentrations of tens of millions of simulated halos to compute a robust $c-M$ relation across a wide range of redshifts and masses. Our $c-M$ relation can be used in preparation for and analysis of next-generation surveys. We then study the relationship between halo formation time and concentration by tracking the evolution of individual halos' masses and concentrations.