Genetic type particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics, information theory, and engineering sciences. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their interacting particle interpretations. In this chapter, we provide an introduction to the stochastic modeling and the theoretical analysis of these particle algorithms. We also illustrate these methods through several applications.