We introduce the multivariate Ornstein-Uhlenbeck and discuss how it generalizes a vast class of continuous-time and discrete-time multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. We illustrate an application to swap contract strategies. Fully documented code illustrating the theory and the applications is available at MATLAB Central.