Catalysts can be broadly classified into homogeneous and heterogeneous types. Homogeneous catalysts are in the same phase as the reactants, often dissolved in the same solvent. They are typically easier to study and can offer high selectivity and activity. However, separating them from the reaction mixture can be challenging. Heterogeneous catalysts, on the other hand, are in a different phase than the reactants, usually solid while the reactants are in liquid or gas phase. They are easier to separate from the reaction mixture but can suffer from issues like deactivation due to surface poisoning.