To date, the Large Hadron Collider has produced more than ten million pairs of top quarks across a broad range of energies. This enormous harvest of the heaviest known elementary particle allows 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 angle 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 LHC data set, and can inform us about models that explain an anomaly in top production at the Tevatron.