The introduction of modern robot-assisted and laparoscopic methods of surgical interventions have extended the range of surgical indications, at the same time as raising a number of specific problems related to the technical features of minimally invasive treatment. This fact makes us consider the effect of surgical aggression on the patient from a new perspective. In particular, the influence of pneumoperitoneum and the patient’s position on venous return, regional blood flow changes, and concomitant shifts of some homeokinetic systems require elucidation. This article reviews the available literature to describe the main features of anesthesia during robot-assisted surgical interventions. Recommendations from systematic reviews and meta-analyses were used. The search depth comprised the period of 12 years (2011–2022). Such factors as antiphysiological position on the operating table, tense carboxyperitoneum, and carboxythorax affect almost all organs and many regulatory mechanisms, thus having a pathological effect on the cardiovascular and respiratory systems, kidney, liver, intestines, blood coagulation system, immune system, and thermoregulation mechanisms. These effects are particularly pronounced in patients with concomitant diseases. In addition to knowledge in the field of pathophysiology, surgeons should be capable of predicting the course of events to take actions aimed at preventing the development of complications. Robot-assisted surgical interventions, although being less traumatic, are characterized by specific features that should be taken into account when preparing a patient to undergo surgery, selecting an optimal method of surgical intervention, and managing the patient in the intra- and postoperative period with rehabilitation.