Summary: In this paper, we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity, see [G. Gentili and D. C. Struppa, C.R., Math., Acad.Sci.Paris 342, No.10, 741–744 (2006; Zbl 1105.30037)], and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.