We consider several interacting strings of characters. Otherwise speaking, we consider one-dimensional random walks interacting with each other and with their environments (mostly in a one-sided manner). This embraces many applications: queueing networks with different customer types, random walks on some discrete non-commutative groups, random Turing machines and others. We present a scheme for the general theory of such processes, the general theory of random walks in the orthant being a particular case. This scheme is being developed in several papers, a review of which is presented here.