Major developments in the analysis of non-stationary time series and cointegration are described in this study. Papers include David Hendry's work on forecasting, Peter Phillip's work on Bayesian models, Svend Hylleberg's work on seasonality, and Adrian Pagan's work on real business cycle models. Other topics covered include an overview of the different estimators of cointegrating relationships, and a new test of cointegration. Applications find roots in macroeconomic series, test the Fisher Hypothesis, test money demand functions, and test for inflation bubbles.