The theme of unit roots in macroeconomic time series have received a great amount of attention in terms of theoretical and applied research over the last three decades. Since the seminal work by Nelson and Plosser (1982), testing for the presence of a unit root in the time series data has become a topic of great concern. This issue gained further momentum with Perron's 1989 paper which emphasized the importance of structural breaks when testing for unit root processes. This paper reviews the available literature on unit root tests taking into account possible structural breaks. An important distinction between testing for breaks when the break date is known or exogenous and when the break date is endogenously determined is explained. We also describe tests for both single and multiple breaks. Additionally, the paper provides a survey of the empirical studies and an application in order for readers to be able to grasp the underying problems that time series with structural breaks are currently facing.