The talk will review the recent literature on stochastic trends and cointegration in large dimensional multivariate time series and present new results on estimation and inference in these systems. The limit distributions of empirical eigenvalues and eigenvectors associated with alternative novel Canonical Correlations Analyses (CCA) will be discussed. It will be shown how these CCA deliver estimators of the number of common trends and of a basis of the common trends loadings space. (Super-)consistency as well as the asymptotic distributions of estimators are derived. The properties of the estimators are compared with existing alternatives both theoretically and via Monte Carlo simulations.