This paper reviews the literature on structural breaks in financial time series. The second section discusses the implications of structural breaks in financial time series for statistical inference purposes. In the third section we discuss change-point tests in financial time series, including historical and sequential tests as well as single and multiple break tests. The fourth section focuses on structural break tests of financial asset returns and volatility using the parametric versus nonparametric classification as well as tests in the long memory and the distribution of financial time series. In concluding we provide some areas of future research in the subject.