In this talk I will report on work on elliptic cohomology with Tomasini and Scherotzke. With Tomasini we give a new construction of equivariant elliptic cohomology in terms of a stack of maps out of the elliptic curve. This construction generalizes beautiful recent work of Moulinos-Robalo-Toen to the equivariant setting, and brings elliptic cohomology closer to well known constructions in algebraic geometry such as (secondary) Hochschild homology. Also it opens the way to possible non-commutative generalizations. With Scherotzke we show that equivariant elliptic cohomology is not a derived invariant, thus confirming the heuristics that elliptic cohomology captures higher categorical information. This depends on a careful analysis of the equivariant elliptic cohomology of toric varieties.