Abstract
In this article, we introduce the product structures and complex structures on hom-Lie superalgebras. First, we give the necessary and sufficient conditions for the existence of product structures and complex structures, respectively. Then, we study special product structures and complex structures, respectively, and accordingly give different decompositions of hom-Lie superalgebras. Finally, as applications of these two structures, we introduce para-Kähler hom-Lie superalgebras and Kähler hom-Lie superalgebras and then obtain some properties.