Abstract: The meshless or meshfree method has progressed rapidely in recentyears. It becomes one of the most important topics in computationalmechanics. With its many special advantages,it is considered as a new generation of numerical methods after finite elementmethod. Up to now, at least several dozens of special methods withdifferent advantages have been proposed. The purpose of this paper is todiscuss several important meshless methods, especially in solid mechanics.The classifications, the constructions of shape functions, the perspective,the advantages and the disadvantages of different methods are discussed,together with some common features.Finally the perspectives and the challenges in developing the meshleshmethods are given.