Updated book or review paper on MCMC methods (2022) For a self-study course, I'm looking for bibliography that describes current MCMC algorithms. I'd prefer a book or a review paper.
My background knowledge is at the level of Gamerman-Lopes or Gilks-Richardson-Spiegelhalter and I will read Liu soon, but I'd like to find other good updated material that will help me understand the current directions of research.

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*The Hastings algorithm at fifty, by Dunson & Johndrow, Biometrika, 2020


*Computational Bayesian Statistics: An Introduction by Carlos Daniel Paulino, M. Antónia Amaral Turkman, & Peter Muller CRC Press, 2020


*Accelerating MCMC algorithms by Christian Robert, Víctor Elvira, Nick Tawn, & Changye Wu, in Wiley Interdisciplinary Reviews: Computational Statistics, 2018


*Markov Chain Monte Carlo Methods, a survey
with some frequent misunderstandings by Christian P. Robert & Wu Changye,  in Wiley StatsRef: Statistics Reference Online, 2020 [where I reproduced some Q&A's from Cross Validated]


*Handbook of Markov Chain Monte Carlo by Steve Brooks, Andrew Gelman, Galin Jones  & Xiao-Li Meng, 2011 [still relevant, see, e.g., the chapter on HMC]
