The evolution of hepatic surgery at the present stage of medical development requires specialists to develop patient-oriented rational surgical tactics and use modern methods for the diagnosis and prediction of post-resection liver failure in the surgical treatment of liver tumors by resection, thereby forming approaches that reduce the risks of severe postoperative complications associated with insufficient liver remnants remaining after extensive resection. The paper reviews the problematic issues of diagnosis and treatment of liver tumors, as well as provides current views on the relevance of timely prevention of post-resection liver failure. The study considers methods for assessing the risks of complications and adverse outcome when planning and performing extensive liver resections, defines the concept of post-resection liver failure, and highlights the main mechanisms of vicarious hypertrophy. The paper examines the most commonly used methods for vicarious hypertrophy of the parenchyma remaining after extensive liver resection, their advantages, and disadvantages. The main possible causes of failures in developing a strategy for two-stage liver resections are analyzed. A critical analysis of available contemporary literature enabled the authors of the paper to identify possible ways to further improve the results of extensive liver resections.