Intrinsic alignments of galaxy shapes with cosmological large-scale structure include a great deal of information about galaxy formation and evolution in a cosmological context, while also serving as a contaminant to weak gravitational lensing measurements (which assume that all coherent galaxy alignments are due to gravitational lensing). In this talk, I will discuss recent progress in our understanding of galaxy intrinsic alignments on both the observational side and the computational side, using SDSS-III BOSS data and SPH simulations, respectively. Recent work using massive BOSS galaxies has permitted a study of how galaxy intrinsic alignments vary from small scales (within massive halos) to cosmological scales, and how the level of the alignments scales with the galaxy environment (for brightest group galaxies, satellites in groups, and field galaxies). Among these new observational results is the fact that the level of small-scale alignments (<1 Mpc/h) correlates more tightly with the large-scale galaxy bias (from >10 Mpc/h) than with the galaxy luminosity. On the computational side, high-resolution SPH simulations with 100 Mpc/h box sizes are able to make predictions for how galaxy intrinsic alignments scale with galaxy properties, as well as to make verifiable predictions for the intrinsic alignment 2-point correlation functions of massive galaxies that are observed by existing galaxy redshift surveys. I will discuss challenges for using and interpreting simulated intrinsic alignment signals, and the latest results for their comparison with observations, as well as the implications for future weak lensing surveys.