1 Introduction  
2 General Framework  
2.1 Vanilla Schemes for Noisy MH and Noisy IS  
2.2 Accelerating and Denoising by Surrogates  
3 Overview and Generic Scheme  
4 Specific Instances of Noisy Monte Carlo Methods  
5 Application Scenarios  
5.1 Likelihood-free Context  
5.2 Application to Reinforcement Learning  
6 Numerical Experiments  
7 Conclusions