In patients with autoimmune diseases, anti-idiotypic antibodies directed to nucleoprotein complexes, DNA, and enzymes that participate in nucleic acid metabolism may be induced spontaneously by primary antigens and can have characteristics of the primary antigen, including catalytic activity. The first natural catalytic antibody, now termed abzyme, which hydrolyzes intestinal vasoactive peptide, was discovered by Paul et al. [Science 244 (1989) 1158]. Subsequently, other abzymes able to hydrolyze proteins, DNA, RNA, or polysaccharides have been found in the sera of patients with autoimmune and also viral pathologies. Further, we have discovered in the milk of healthy human mothers antibodies that catalyze the hydrolysis of RNA, DNA, nucleotides, and the phosphorylation of lipids and proteins. The phenomenon of catalysis by autoantibodies is extremely interesting and can potentially be applied to many different objectives including new types of efficient catalysts, evaluation of the functional roles of abzymes in innate and adaptive immunity, and understanding of certain aspects of self-tolerance and of the destructive responses in autoimmune diseases. In this review, we collate methods for purifying and characterizing natural abzymes especially those catalyzing DNA and RNA hydrolysis. We also describe new methods that we have developed to provide rigorous criteria that catalytic activity is an intrinsic property of some antibodies. Some major current themes are discussed as well as potential applications of abzymes in scientific, medical, and biotechnological fields.