Conformal techniques in Riemannian and Lorentzian geometry

After giving an overview over some recently developed conformal methods in Riemannian and Lorentzian geometry, we focus on a result of a joint work with Marc Nardmann (Dortmund) stating that every conformal class contains a metric of bounded geometry. Finally, we sketch implications of the result in the theory of the Yamabe flow on noncompact manifolds.