The Caulton-Eisenstein rules are a set of guidelines that assist in predicting the reactivity and stability of organometallic compounds based on their electronic and steric properties. These rules help in understanding how different organometallic compounds will behave in chemical reactions, particularly in substitution reactions, and how they can be synthesized effectively. By considering factors like the nature of the metal center and the ligands attached, these rules streamline the process of designing and working with various organometallic compounds.