This should be an exposition that is fairly accessible. I will review coupling as a methodology for computing with Markov chains. This has had many payoff, from the understanding of mixing properties and then to the path Central Limit Theorems. It has been very useful in statistical physics and showing connectivity of random structures. It is also the natural tool for a looking at a Markov Chain with additional structure because they arise in a certain natural way: as the independent and identically distributed composition of random transformations. This object exploded fractals (and by association chaos theory) into the everyday realm of human consciousness.