**I** have recently [well, not so recently!] been asked to write a review paper on ways of accelerating MCMC algorithms for the [review] journal WIREs Computational Statistics and would welcome all suggestions towards the goal of accelerating MCMC algorithms. Besides [and including more on]

- coupling strategies using different kernels and switching between them;
- tempering strategies using flatter or lower dimensional targets as intermediary steps, e.g., à la Neal;
- sequential Monte Carlo with particle systems targeting again flatter or lower dimensional targets and adapting proposals to this effect;
- Hamiltonian MCMC, again with connections to Radford (and more generally ways of avoiding rejections);
- adaptive MCMC, obviously;
- Rao-Blackwellisation, just as obviously (in the sense that increasing the precision in the resulting estimates means less simulations).