This chapter reviews inference about large autoregressive or moving average roots in univariate time series, and structural change in multivariate time series regression. The "problem" of unit roots is cast more broadly as determining the order of integration of a series; estimation, inference, and confidence intervals are discussed. The discussion of structural change focuses on tests for parameter stability. Much emphasis is on asymptotic distributions in these nonstandard settings, and one theme is the general applicability of functional central limit theory. The quality of the asymptotic approximations to finite-sample distributions and implications for empirical work are critically reviewed.