The past 50 years have witnessed a remarkable development in portfolio selection both in theory and real practice. With a rapid globalization of world economy and a fast growth of capital markets in China , more and more domestic financial institutes start to feel an urgent need of applying modern portfolio selection theory to their prac2 tice. This paper aims at reviewing the fundamental concepts and basic solution methodologies in portfolio selection and examining recent development in the field. It is hoped that the research issues brought up in the paper will stimulate more interests in the development of portfolio selection , thus advancing the state2of2the2art of risk manage2 ment and financial optimization in China.