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Solving JSSP is an intractable subject. It has great significance in improving productive efficiencies for manufacture enterprise. In recent decades, designing algorithms for solving problem of JSSP problem become an important issue. Moreover, it is difficult to find an appropriate criteria to evaluate efficiency of algorithms available with respect to solving JSSP. Various algorithms for solving JSSP are listed, and their advantages and disadvantages are also indicated. At the same time, three critical element for designing algorithms for JSSP were proposed. Finally, several future research trends of solving job shop problems and proposals for the future research work are summarized and presented respectively.