Liver diseases, characterized by high morbidity and mortality, represent a substantial medical problem globally. The current therapeutic approaches are mainly aimed at reducing symptoms and slowing down the progression of the diseases. Organ transplantation remains the only effective treatment method in cases of severe liver pathology. In this regard, the development of new effective approaches aimed at stimulating liver regeneration, both by activation of the organ’s own resources or by different therapeutic agents that trigger regeneration, does not cease to be relevant. To date, many systematic reviews and meta-analyses have been published confirming the effectiveness of mesenchymal stromal cell (MSC) transplantation in the treatment of liver diseases of various severities and etiologies. However, despite the successful use of MSCs in clinical practice and the promising therapeutic results in animal models of liver diseases, the mechanisms of their protective and regenerative action remain poorly understood. Specifically, data about the molecular agents produced by these cells and mediating their therapeutic action are fragmentary and often contradictory. Since MSCs or MSC-like cells are found in all tissues and organs, it is likely that many key intercellular interactions within the tissue niches are dependent on MSCs. In this context, it is essential to understand the mechanisms underlying communication between MSCs and differentiated parenchymal cells of each particular tissue. This is important both from the perspective of basic science and for the development of therapeutic approaches involving the modulation of the activity of resident MSCs. With regard to the liver, the research is concentrated on the intercommunication between MSCs and hepatocytes under normal conditions and during the development of the pathological process. The goals of this review were to identify the key factors mediating the crosstalk between MSCs and hepatocytes and determine the possible mechanisms of interaction of the two cell types under normal and stressful conditions. The analysis of the hepatocyte–MSC interaction showed that MSCs carry out chaperone-like functions, including the synthesis of the supportive extracellular matrix proteins; prevention of apoptosis, pyroptosis, and ferroptosis; support of regeneration; elimination of lipotoxicity and ER stress; promotion of antioxidant effects; and donation of mitochondria. The underlying mechanisms suggest very close interdependence, including even direct cytoplasm and organelle exchange.