We need to reason about rankings of objects in a wide variety of domains including information retrieval, sports tournaments, bibliometrics, and statistics. We propose a global constraint therefore for modeling rankings. One important application for rankings is in reasoning about the correlation or uncorrelation between sequences. For example, we might wish to have consecutive delivery schedules correlated to make it easier for clients and employees, or uncorrelated to avoid predictability and complacence. We therefore also consider global correlation constraints between rankings. For both ranking and correlation constraints, we propose efficient filtering algorithms and decompositions, and report experimental results demonstrating the promise of our proposed approach.