We will discuss relative oscillation theory for general Sturm-Liouville differential expressions and prove perturbation results and invariance of essential spectra in terms of the real coefficients p, q, r. The novelty here is that we also allow perturbations of the weight function r in which case the unperturbed and the perturbed operator act in different Hilbert spaces. This is based on joint work with Jussi Behrndt, Philipp Schmitz, and Carsten Trunk.