| Two subschemes V and V' without common components in projective space are *linked* if their union is a complete intersection. Allowing finite chains of linkages gives an equivalence relation called *liaison*. For subschemes of codimension 2 in projective space there is a highly developed and satisfying theory of liaison equivalence classes. In higher codimension, this definition is too strict to give comparable analogous results, but if one replaces "complete intersection" by "arithmetically Gorenstein scheme" in the above definition, the resulting *Gorenstein liaison* promises to give a suitable theory. I will report on recent results and open problems in this area. |