The parameter space of superconformal field theories associated to K3 can be understood as an extension of the parameter space of Einstein metrics on K3. We begin our talk by explaining this result, which goes back to Aspinwall and Morrison, in terms of geometric data. Then we show that a precise understanding of the geometric derivation of this parameter space allows to determine within it the location of theories obtained by orbifold constructions. In particular, the only parameter without naive geometric interpretation, the B-field, receives an interpretation in terms of the classical McKay correspondence for orbifolds.