Abstract Simulation of interacting particle systems has been a well established method for many years now. Such systems can span different scales, including microscopic (where particles represent atoms, as in Molecular Dynamics simulations) as well as macroscopic. In the latter case, growing interest is put into Smoothed Particle Hydrodynamics approach. Traditionally, over many years, simulation of particle systems of a size big enough to give reasonable physical results, have been treated as the most time consuming calculations. As such, they have been run in an off-line mode, even in largest computer centers, where the batch mode work was a general rule. Introduction of massively parallel graphics processors (GPUs) gave an incredible impact not only to rendering performance, but also to the speed of numerical calculations, available also on a desktop computer or a local cluster. This enabled very fast (real-time or near real-time) simulations on a personal or near personal hardware for relatively large systems. It also encouraged to make the simulations interactive, with parameters adjusted on-line as well as to use on-line interactive visualization. The price for the speed is the necessity of designing new data structures and new algorithms which are vital for efficient use of massively parallel GPUs. Thanks to available software: Nvidia's CUDA and more general OpenCL, GPU programming became easier, however still needs a significant effort.