The economic advantages of continuous processing of biopharmaceuticals, which include smaller equipment and faster, efficient processes, have increased interest in this technology over the past decade. Continuous processes can also improve quality assurance and enable greater controllability, consistent with the quality initiatives of the FDA. Here, we discuss different continuous multi-column chromatography processes. Differences in the capture and polishing steps result in two different types of continuous processes that employ counter-current column movement. Continuous-capture processes are associated with increased productivity per cycle and decreased buffer consumption, whereas the typical purity-yield trade-off of classical batch chromatography can be surmounted by continuous processes for polishing applications. In the context of continuous manufacturing, different but complementary chromatographic columns or devices are typically combined to improve overall process performance and avoid unnecessary product storage. In the following, these various processes, their performances compared with batch processing and resulting product quality are discussed based on a review of the literature. Based on various examples of applications, primarily monoclonal antibody production processes, conclusions are drawn about the future of these continuous-manufacturing technologies.