In Chap. 9, we describe the coupling algorithm for regenerative processes and present ergodic theorems for regenerative processes with explicit upper bounds for convergence rates in these theorems. We present alternative equivalent definitions of a regenerative process with a transition period, consider renewal equations for one-dimensional distributions of the regenerative process, show that the characteristics of the regenerative process related to its transition period can be chosen in the way providing stationarity of one-dimensional distributions of the regenerative process, and present a coupling algorithm for regenerative processes. These results let us obtain the main ergodic for regenerative processes with explicit power and exponential upper bounds for variational distances between one-dimensional distributions of regenerative processes and the corresponding stationary distributions, using upper bounds for power and exponential moments of coupling times for renewal schemes.