The importance of a priori check of the existence of unit roots in the panel data comes from the already known effect that the presence of unit roots in time series may cause a misinterpretation of estimated results. Adding the cross-section dimension to the time series dimension offers an advantage in testing for nonstationary and cointegration since cross-section increases the data set used in those tests, thus improving their power. However, the cross-section dimension also brings some new problems into question, namely the existence of cross-section dependency which can bias usual panel data unit root test results in small samples. This paper presents a survey of panel unit root tests, evidencing the most recent developments on the issue, including those that account for the presence of contemporaneous cross-correlation as well as for the presence of heterogeneous serial correlation. Parallel to the developments of panel unit root tests, great attention has also been given to cointegration tests. We briefly review the most widely referred cointegration tests. We apply the reviewed panel unit root tests on an EU social variable which represents the population weight over than 65 years of age. We consider data running from 1970 to 2001. The panel unit root test results reveal to be sensitive to the prior assumptions regarding contemporaneous cross-correlation and heterogeneous serial correlation in small samples. The usual battery of panel unit root tests appear not to be adequate when a panel is composed by a mix of a stationary and nonstationary time series.