The field of three-dimensional computational Vortex Elements Methods (VEMs) has matured considerably. VEMs are a means of simulating time dependent, incompressible fluid flow in which the flow is represented by a collection of vorticity elements. The vorticity elements concentrate in the flow region of interest where the vorticity is concentrated. This feature makes the method very attractive for complex flow simulations. In this paper a brief introduction to three-dimensional vortex methods for flows of incompressible nature are provided with a special emphasis on the Vortex Particle Method so called Vortons Method. The paper reports results for the simulation of various kinds of vortex ring interactions. The new results and evidence on the possibility of simulating turbulent flows in the inertial range by using the vorton representation of the vorticity field are also presented.