Chemical reactions between dysprosium and carbon were studied in laser-heated diamond anvil cells at pressures of 19, 55, and 58 GPa and temperatures of similar to 2500 K. In situ single-crystal synchrotron X-ray diffraction analysis of the reaction products revealed the formation of novel dysprosium carbides, Dy4C3 and Dy3C2, and dysprosium sesquicarbide Dy2C3 previously known only at ambient conditions. The structure of Dy4C3 was found to be closely related to that of dysprosium sesquicarbide Dy2C3 with the Pu2C3-type structure. Ab initio calculations reproduce well crystal structures of all synthesized phases and predict their compressional behavior in agreement with our experimental data. Our work gives evidence that high-pressure synthesis conditions enrich the chemistry of rare earth metal carbides.