To date, the LHC has already made over one million pairs of top quarks, with energies spanning from production threshold into the truly TeV regime. The large statistics and broad energy bandwidth of the LHC will allow us to study the physics of top quark production with unprecedented detail, hopefully yielding surprises along the way. Towards this end, I will introduce simple observables that are sensitive to spin interference effects in top quark production, based on the azimuthal angular patterns of the tops' decay products. Besides opening a clean and unique window on the nontrivial correlations of top spins within the Standard Model, such observables can be used to categorize or even discover various types of new physics. I will argue that azimuthal correlations are potentially observable with very high significance in multiple channels using the current data set.