Cylindrical symmetry allows for potentially significant astrophysical applications. Even the general relativistic vacuum is quite rich, including a static ground state, the Levi–Civita spacetime and multiple types of Einstein–Rosen exact wave solutions. We summarize our recent study on the interpretation of the static background, then proceed to discuss the backreaction of the cylindrical waves at second order, in the WKB approximation and under the Brill–Hartle averaging scheme, identifying the lasting effect of a passing wave on the background as an emerging exact radiative spacetime. We also briefly discuss extensions of the Einstein–Rosen waves in generalized Brans–Dicke theories, where the scalar field is sourcing these waves.