The Monte Carlo method, as an effective tool for approximating integrals and simulating reality, has been widely applied across numerous scientific fields to solve complex computational problems. It first appeared in early days (1945-55) of electronic computing. The technique was named after the famed gambling resort because its procedures incorporate the element of chance. Initially, statistical physicists introduced a Markov Chain-based dynamic Monte Carlo method for the simulation of simple fluids. This method was later named as “Markov chain Monte Carlo (MCMC)” and extended to cover more and more complex physical systems. At almost the same time, a sequential (recursive) construction was proposed to simulate long chain polymers, which can be seen as the ancestor of the popular “particle filters” (aka sequential Monte Carlo). Nowadays, Monte Carlo has been widely used as a powerful computational tool for optimization and integration in diverse fields, especially for various AI tasks. We will first review of Monte Carlo’s history, and then discuss a few recent directions and developments, e.g. Monte Carlo tree search, reparameterization, diffusion sampling, resampling and optimal transport, and particle flow via variational approximation.