It is the aim of the present chapter to collect some of the operations which preserve the class of hyponormal operators. We have already seen in Example II.2.1 that the square of a hyponormal operator may not be hyponormal. Thus the analytic functional calculus is excluded from these operations. Instead, the main tools in transforming hyponormal operators are the rectangular (and polar) cuttings, which originate in the work of Putnam. The main part of this chapter is devoted to them. We shall also be interested in spectral mappings results, i.e. in how the spectrum transforms under these operations. For an excellent and comprehensive report on these topics we refer to the book of Xia [3].