Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with many degrees of freedom. In this talk I will review recent breakthroughs in constructing discrete- and continuous-time quantum thermodynamic analogues to Glauber and Metropolis dynamics that is 

(i) exactly detailed balanced, 

(ii) efficiently implementable, and 

(iii) quasi-local for geometrically local systems. 

Physically, these constructions resemble the dissipative dynamics arising from weak system-bath interaction. We hope that these natural quantum generalizations of the highly successful Metropolis algorithm will soon play an important role in useful quantum applications.