In this talk, we are concerned with circuit Markov chains, which are generated by weighted circuits. First we will investigate some stochastic properties, with results including the recurrence and reversibility criteria in terms of weighted circuits and the formula of entropy production rate. Then I will introduce the rotational problem of Markov processes, concerning the representations of stochastic matrices by rotational systems. The problem was first proposed by Joel E. Cohen in 1981, and the general answer was given by S. Alpern in 1983. Finally I will present some new results and interpretations of circuit processes in terms of spectral theory and Banach spaces.