Perturbative predictions by quantum field theory about quantum scattering of elementary particles, implied by a corresponding Lagrangian density, are computed using the Feynman rules, a regularization method to circumvent ultraviolet divergences so as to obtain finite results for Feynman diagrams containing loops, and a renormalization scheme. Regularization method results in regularized n-point Green's functions (propagators), and a suitable limiting procedure (a renormalization scheme) then leads to perturbative S-matrix elements. These are independent of the particular regularization method used, and enable one to model perturbatively the measurable physical processes (cross sections, probability amplitudes, decay widths and lifetimes of excited states). However, so far no known regularized n-point Green's functions can be regarded as being based on a physically realistic theory of quantum-scattering since the derivation of each disregards some of the basic tenets of conventional physics (e.g., by not being Lorentz-invariant, by introducing either unphysical particles with a negative metric or wrong statistics, or discrete space-time, or lowering the dimensionality of space-time, or some combination thereof). So the available regularization methods are understood as formalistic technical devices, devoid of any direct physical meaning. In addition, there are qualms about renormalization. For a history and comments on this more than half-a-century old open conceptual problem, see e.g.