The application of Monte Carlo techniques to Bayesian state estimation is discussed. A simple theory for the Monte Carlo uncertainty is given and recursive Monte Carlo filters for general non-linear systems constructed from basic considerations. The methods are applied to a non-linear pendulum with measurement saturation and to bearings-only target tracking. The parameters of the measurement noise are in the bearings example determined on-line as part of the state estimation. The state vector then becomes six-dimensional, but the problem is still handled in real time. There is scope for improvement. Filter performance hinges on certain probability density estimates running in parallel with the filters. Errors in the estimated densities lead to filter inaccuracies that must be compensated by raising the number of Monte Carlo samples. Better ways of estimating the densities may lower this number and enhance speed.