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The complexity of transplant medicine pushes the boundaries of innate, human reasoning. From networks of immune modulators to dynamic pharmacokinetics to variable postoperative graft survival to equitable allocation of scarce organs, machine learning promises to inform clinical decision making by deciphering prodigious amounts of available data. This paper reviews current research describing how algorithms have the potential to augment clinical practice in solid organ transplantation. We provide a general introduction to different machine learning techniques, describing their strengths, limitations, and barriers to clinical implementation. We summarize emerging evidence that recent advances that allow machine learning algorithms to predict acute post-surgical and long-term outcomes, classify biopsy and radiographic data, augment pharmacologic decision making, and accurately represent the complexity of host immune response. Yet, many of these applications exist in pre-clinical form only, supported primarily by evidence of single-center, retrospective studies. Prospective investigation of these technologies has the potential to unlock the potential of machine learning to augment solid organ transplantation clinical care and health care delivery systems.