L-asparaginase, which hydrolyzes asparagine and, to a lesser extent, glutamine, initially used to treat acute lymphoblastic leukemia and other hematological malignancies, may soon become a therapeutic agent for the treatment of a wide group of oncological diseases, as more and more evidence is accumulating that not only leukemia cells and lymphomas but also various solid tumors are sensitive to the action of this enzyme. However, like any other drug, L-asparaginase is not always effective; moreover, its use often leads to unwanted side reactions. Taking this into account, for the successful use of asparaginase, it is advisable to study and introduce into clinical practice prognostic markers that make it possible to predict in advance its effectiveness in the treatment of a particular patient. This review highlights various biochemical factors that influence the sensitivity of tumor cells to L-asparaginase. The asparagine synthetase and glutamine synthetase genes are examined in detail; the influence of their expression levels on the sensitivity of tumors to asparaginase has been studied in numerous experiments. In addition, “nonclassical” factors are considered, such as the expression of glutamine transporter genes, opioid receptors, methylation of the asparagine synthetase gene promoter, the activity of some signaling pathways, and the activity of the PTEN protein. The presented data can contribute to the creation of a more holistic and accurate system of markers that can be used to predict the sensitivity of tumor cells, including solid ones, to L-asparaginase.