The mathematically rigorous construction of quantum field theories
beyond perturbation theory is one of the main challenges of QFT. In this talk
I will review approaches to this problem that are based on concepts from
"algebraic quantum field theory" (AQFT), a framework based on algebras of
observables localized in open regions in spacetime instead of point-like
localized quantum fields. The talk will hence also present the main features of
AQFT and review ideas, results and open problems in the subject.