  The goal of this paper is to give a short and self contained proof of general
bounds for subgeometric rates of convergence, under practical conditions. The
main result whose proof, based on coupling, provides an intuitive understanding
of the results of Nummelin and Tuominen (1983) and Tuominen and Tweedie (1994).
To obtain practical rates, a very general drift condition, recently introduced
in Douc et al (2004) is used.
