This survey paper discusses the Cointegrated VAR methodology and how it has evolved over the last 30 years. The first section is a description of major steps in the econometric development of the CVAR model that facilitated serious real world applications. The next three sections are primarily methodological and discuss (i) difficulties and puzzles when confronting theory with the data, (ii) the formulation of a viable link between theory and the data, a so called theory-consistent CVAR scenario, and (iii) how all this was inspired by Trygve Haavelmo and his Nobel prize winning monograph "The Probability Approach to Economics". The next two sections discuss early applications of the Cointegrated VAR model to monetary transmission mechanisms, international transmission mechanisms and wage, price and unemployment dynamics. They report puzzling evidence, discuss the need for new theory, and propose a method for combining partial CVAR analyses into a larger macroeconomic model. The following sections propose a new, empirically-based, approach to macroeconomics in which imperfect knowledge based expectations replace so called rational expectations and in which the financial sector plays a key role for understanding the long persistent movements in the data. The last section argues that the CVAR can act as a "design of experiment for passive observations" and illustrates with several applications including unemployment dynamics under crises periods and aid effectiveness in South Saharan African countries.