Unprojection or "constructing bigger Gorenstein ideals from smaller one" is an algebraic device for constructing Gorenstein varieties in codimension 4, 5, ..., beyond the range of standard structure theorems; it has a large number of fairly automatic applications to the construction of certain types of surfaces, 3-folds and so on, including some examples where the deformation theory is obstructed. The theory is an elegant piece of commutative algebra, but the applications usually get into explicit calculations that are often fairly messy and a lot of fun.
