This monograph presents some new concentration inequalities for Feynman-Kac particle processes.It analyzes different types of stochastic particle models, including particle profile occupationmeasures, genealogical tree based evolution models, particle free energies, as well asbackward Markov chain particle models. It illustrates these results with a series of topics relatedto computational physics and biology, stochastic optimization, signal processing and Bayesianstatistics, and many other probabilistic machine learning algorithms. Special emphasis is givento the stochastic modeling, and to the quantitative performance analysis of a series of advancedMonte Carlo methods; including particle filters, genetic type island models, Markov bridgemodels, and interacting particle Markov chain Monte Carlo methodologies.