Many complex mixtures usually constitute hundreds or even thousands of individual components of interest. Such mixtures are much too complicated to be separated for analytical duties in a reasonable period of time using only a single-dimensional chromatographic method. However, if a complex mixture is separated by an initial dimension using multi-dimensional liquid chromatography, a simpler portion of that separation is collected and goes to the second dimension. Each of these fractions will be analyzed separately, allowing exceedingly complex mixtures to be resolved in a short period of time. This chapter explains the fundamental principles, theoretical discussions as well as various applications with typical examples of multi-dimensional liquid chromatography in different fields.