Catalytic antibody (also known as abzyme) is a kind of immunoglobulin with catalytic activity. Because it has high selectivity and amazing diversity as antibodies and highly catalytic activities as enzymes, it is anticipated that using abzyme preparation technology one can obtain any kind of tailor-made biocatalysts, including those not occurred in nature, for various kinds of practical applications. Thus, abzyme study has an important value in theory and practice for biology, chemistry and medicine etc. The new advances of catalytic antibody research are summarized with a special emphasis on the breadth and scope of new antibody-catalyzed reactions and novel hapten design strategies. The problems to be solved in this field are discussed and the strategies for solving these problems are presented with special focus on increasing the catalytic activities of abzymes.