Unit roots are nonstationary autoregressive (AR) or autoregressive moving average (ARMA) time series processes which may include an intercept and/or a trend. These processes are used often in economics and finance, but can also be found in other scientific fields. Unit root tests address the null hypothesis of a unit root, and an alternative hypothesis of a stationary (or trend stationary) time series. Critical values for unit root tests are typically derived via simulation of limiting distributions expressed as functionals of Brownian motions. The critical values for the Dickey Fuller unit root test with a constant and linear trend are derived via simulation in the R language. Simulation studies are presented showing that linear regressions with unit root processes often produce spurious results. Additional simulation studies are reviewed providing statistical evidence that near‐unit roots can often result in spurious cointegration relationships. Various unit root tests are presented, including ones that allow for structural breaks in intercept and/or trend. Threshold unit root tests are introduced. Simulation studies are used to compare the unit root tests under various scenarios. The case where the analyzed time series may have stationary and nonstationary segments is also considered. WIREs Comput Stat 2017, 9:e1396. doi: 10.1002/wics.1396This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data