  We review the Random Batch Methods (RBM) for interacting particle systems
consisting of $N$-particles, with $N$ being large. The computational cost of
such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods
use small but random batches so the computational cost is reduced, per time
step, to $O(N)$. In this article we discuss these methods for both classical
and quantum systems, the corresponding theory, and applications from molecular
dynamics, statistical samplings, to agent-based models for collective behavior,
and quantum Monte-Carlo methods.
