This introductory paper aims to provide an overview of Monte Carlo methods, with a focus on their application in probabilistic machine learning. It reviews the fundamental building blocks of modern Markov chain Monte Carlo (MCMC) simulation, discusses the historical development of MCMC algorithms, and highlights new research directions. The paper emphasizes the importance of domain-specific knowledge in designing efficient MCMC algorithms and explores various sampling techniques, including rejection sampling, importance sampling, and MCMC methods such as the Metropolis-Hastings algorithm, simulated annealing, Gibbs sampling, and hybrid Monte Carlo. It also introduces the concept of reversible jump MCMC for model selection problems. The paper concludes by outlining the potential of combining MCMC with machine learning algorithms to address complex inference and learning tasks.This introductory paper aims to provide an overview of Monte Carlo methods, with a focus on their application in probabilistic machine learning. It reviews the fundamental building blocks of modern Markov chain Monte Carlo (MCMC) simulation, discusses the historical development of MCMC algorithms, and highlights new research directions. The paper emphasizes the importance of domain-specific knowledge in designing efficient MCMC algorithms and explores various sampling techniques, including rejection sampling, importance sampling, and MCMC methods such as the Metropolis-Hastings algorithm, simulated annealing, Gibbs sampling, and hybrid Monte Carlo. It also introduces the concept of reversible jump MCMC for model selection problems. The paper concludes by outlining the potential of combining MCMC with machine learning algorithms to address complex inference and learning tasks.