Physics-based simulation is one of the most intensively studied fields in recent decades, and currently there are many wonderful techniques, especially to simulate the dynamics of solids, fluids, and the interaction between them. In order to simulate rigid solids, classical methods based on the application of forces or impulses are used. On the other hand, response to detected contacts or collisions requires using fast and efficient techniques, and position-based methods have become popular. These research fields have become very popular in the Computer Graphics community. Currently, the methods have evolved to be more accurate, fast, stable, and controllable, but more complex to implement, which makes them adequate for use in interactive environments like computer games, virtual reality applications, and to generate special effects in movies. In this research work, we show some position-based methods which are well-suited for the simulation of solids (rigid and deformable) and fluids. We will use particles as small spheres, and the concept of position-based dynamics is entirely referred to them. Also we show the implementation of several techniques proposed in the last decade, for instance, simulation based on shape matching, Smooth Particle Hydrodynamics (SPH) approach for liquids, Impulse-based dynamics, and the interaction between them. In addition, we will go into some detail in the implementation of these methods with practical examples that demonstrate how useful they are for interactive applications.