A wealth of two-hadron scattering amplitudes have been computed in lattice QCD using finite-volume effects of individual two-hadron states. This however becomes unfeasible for inclusive amplitudes, where many contributing states are summed over. I will discuss the recent status of an alternative approach: applying spectral reconstruction algorithms to treat the ill-posed inverse problem of inferring continuous spectral densities from lattice computations of Eulcidean correlation functions at a finite number of space-time arguments with statistical errors. After presenting a validation of this `brute-force' analytic continuation in the two-dimensional non-linear sigma model, results for isovector vector and axial current-current correlators in QCD are discussed. Such novel computations offer many advantages, including the first-principles determination of the R-ratio and hadron tau decay rates.