Ising lattices model spatial interaction among binary variables, and consequently, are relevant to many scientific disciplines. They are intuitively appealing models because their conditional distributions are given locally (they are Markov fields). On the other hand, their marginal distributions (even for pairs of sites, let alone triples, etc.) are relatively intractable. Indeed, even for the simplest Ising model it is remarkably difficult to obtain the correlation structure (cf. Kaufmann and Onsager (1949), Hurst and Green (1960)). Furthermore, general Ising models are not amenable to direct simulation. Recently, a number of articles have appeared which consider rather specialized binary lattice processes (cf. Bartlett (1967), Besag (1972), Welberry and Galbraith (1973), (1975), Galbraith and Walley (1976), Welberry (1977), Verhagen (1978), Enting (1977), Pickard (1977a)). These models admit direct simulation and have relatively simple marginals. For the most part, however, this work has been rather fragmentary and heuristic. The purpose of the present paper is to report briefly the beginnings of a unified theory (Pickard (1977b)). Proofs are omitted as there is insufficient space. A more detailed account will appear elsewhere.