In this talk I will present algebraic models for equivariant cohomology of quantum group (co)actions on noncommutative spaces. I will start by recalling basic fact of classical equivariant cohomology and discussing Weil and Cartan models for its definition. Then I will move to noncommutative geometry introducing some basic ideas we need from the theory of quantum groups. Finally I will focus on two different kind of deformations, Drinfeld twists and Drinfeld-Jimbo quantum enveloping algebras, discussing similarities and differences of their equivariant models.