Renal replacement therapies (RRTs) represent a cornerstone in the management of severe acute kidney injury. This area of intensive care and nephrology has undergone significant improvement and evolution in recent years. Continuous RRTs have been a major focus of new technological and treatment strategies. RRT is being used increasingly in the intensive care unit, not only for renal indications but also for other organ-supportive strategies. Several aspects related to RRT are now well established, but others remain controversial. In this review, we review the available RRT modalities, covering technical and clinical aspects. We discuss several controversial issues, provide some practical recommendations, and where possible suggest a research agenda for the future.