  In this survey, we describe controlled interacting particle systems (CIPS) to
approximate the solution of the optimal filtering and the optimal control
problems. Part I of the survey is focussed on the feedback particle filter
(FPF) algorithm, its derivation based on optimal transportation theory, and its
relationship to the ensemble Kalman filter (EnKF) and the conventional
sequential importance sampling-resampling (SIR) particle filters. The central
numerical problem of FPF -- to approximate the solution of the Poisson equation
-- is described together with the main solution approaches. An analytical and
numerical comparison with the SIR particle filter is given to illustrate the
advantages of the CIPS approach. Part II of the survey is focussed on adapting
these algorithms for the problem of reinforcement learning. The survey includes
several remarks that describe extensions as well as open problems in this
subject.
