Immune checkpoint inhibitors have opened up new possibilities in clinical oncology. Monoclonal antibodies have shown their high clinical efficiency. They block CTLA-4, PD-1, and PD-L1 receptors and activate the immune response. Many patients have stable and even complete responses. However, some patients have primary or acquired resistance. Therefore, the treatment results in this category of patients are not predictable. Mechanisms of resistance to immune checkpoint inhibitors have not been definitively studied. Many theories try to explain the mechanisms of this phenomenon. Our study aimed to structure and combine the data into groups depending on the etiological factor that reduces the immune response. In addition, based on understanding the mechanisms of resistance and the results of recent clinical studies, we aimed to identify the main ways to overcome it. Therefore, mechanisms that lead to resistance may be associated with tumor properties, tumor microenvironment, or patient characteristics. Tumor properties that reduce the immune response include a) low tumor mutation burden and loss of tumor neoantigens, b) changes in the processing or presentation of neoantigens, and c) changes in signaling pathways of tumor development and epigenetic modifications in genes. The tumor microenvironment is represented by stromal and immune cells, extracellular matrix, cytokines, and blood vessels. Each structure can enhance or reduce the immune response and contribute to the acquired resistance to immune checkpoint inhibitors. The effectiveness of the treatment depends not only on the cells in the tumor microenvironment but also on the metabolic background. In addition, the basic characteristics of the patient ( gender, gut microbiota, HLA-I genotype) can modify the immune response. Based on knowledge about the mechanisms of resistance to immune checkpoint inhibitors, several therapeutic strategies aimed at activating antitumor activity have been evaluated. All of them are based on combining immune checkpoint inhibitors with other drugs. One of the most common options is a combination of PD-1/PD-L1 and CTLA-4 inhibitors. Alternative immune checkpoints are TIM-3, LAG-3, TIGIT and VISTA. Combining immunotherapy with chemotherapy, targeted therapy, neoangiogenesis inhibitors, epigenetic modifiers, PARP or TGF-β inhibitors enhances antitumor response by preventing depletion of effector T cells, enhancing T cell infiltration in the tumor, changes on the tumor microenvironment, and decreasing the accumulation of immunosuppressive cells. This review explores the biological mechanisms of resistance and potential ways of solving this problem.