Continuous renal replacement therapy (CRRT) is a family of extracorporeal treatments which have evolved from simple to complex goals. It began as a monotherapy to lower intravascular volume in an already hemodynamically compromised hypotensive patient. Modern day therapies using the same catch-all name now have lofty goals of reversing the pathophysiology of intermediary metabolism and immunologic disorders. Over several decades a confusing set of abbreviations have emerged. Problems arise when the simpler forms are used for complex goals and vice versa. Presented here is an attempt to simplify the understanding of this heterogeneous therapy by a review of the historical evolution, a review of the goals of subtypes of CRRT, and a review of current cutting-edge therapies which combine renal replacement with other organ rescue therapies. This last management strategy is now becoming commonly known as tandem therapy or multi-system organ support (MOST) therapy. Tandem therapies combine two organ support modalities, and MOST therapy simultaneously uses more than two organ rescue treatments.