This chapter focusses on the polishing steps encountered during protein purification by chromatography. The first part provides a detailed description of the mechanistic phenomena at stake, whose complexity may greatly vary from one case to the other depending on the number and type of impurities, the selectivity for the target protein as well as non-linear and competitive effects. Several multi-column counter-current processes allowing the implementation of the polishing steps in a continuous manner are presented in the second part of the chapter. Modifications of the classical SMB process introduced to better cope with the specific needs of the biopharmaceutical industry are discussed. These modifications primarily aim at recovering more than two fractions and at implementing modifier concentration gradients. Two process design approaches for multi-column processes are presented: an empirical one, which provides a first guess of the operating conditions from single-column experiments, and a model-based one, which allows a more rigorous determination of the process variables. The model-based approach is used to compare the performance of multi-column and single-column processes.