In this talk I will give an overview of perturbative algebraic quantum field theory, which is new framework for rigorous construction of models in QFT. It combines the methods of perturbation theory (e.g. expansion into Feynman graphs) with the axioms of algebraic quantum field theory. This allows to build QFT models in a wide range of examples, including QFT on curved spacetimes. I will report on the latest results obtained within this framework and discuss perspectives for further research.