Monoclonal antibodies (mAbs) are biomolecules of great scientific and practical significance. In contrast to polyclonal antibodies from immune sera, they are homogeneous and monospecific, since they are produced by hybridoma cells representing a clone arising from a single cell. The successful technology was described for the first time in 1975; the inventors were later awarded the Nobel Prize. Currently, mAbs are broadly used as a research tool, in diagnostics and medicine in particular for the treatment of cancer or in transplantology. About 47 therapeutics based on monoclonal antibodies are now available in the US and Europe, and the number is still growing. Production of monoclonal antibodies is a multistage, time-consuming and costly process. Growing demand for these molecules creates space for research focused on improvements in hybridoma technology. Lower costs, human labor, and time are important goals of these attempts. In this article, a brief review of current methods and their advances is given.