Abstract: Smoothed particlehydrodynamics (SPH) is a Lagrangian meshfree particle method, andhas been widely applied to different areas in engineering andscience. SPH method uses a set of particles to discretize thecomputational domain and to represent the state of the systembeing modeled, and approximates the governing equations based onthe set of particles. This paper provides an overview on thedevelopment, numerical aspects, and applications of the SPHmethod. The basic concepts, consistency, boundary treatment,stability and computational efficiency of the SPH method have beendiscussed. Applications of the SPH method to compressible andincompressible fluid flows as well as to rapid deformation andfailure of elastic-plastic materials have been addressed. Finallythe paper concludes with remarks of the merits and defects of theSPH methods, and with some predictions of numerical methoddevelopment and application areas.