The search for the sources of high-energy cosmic rays (CRs) has made significant progress the past decade. By including multimessenger methods, the general picture of the presence of a Galactic component at low energies and an extragalactic one at the highest energies has been strengthened. Yet, unambiguous proof of the exact origins of CRs is missing. In this review, the current scientific status on Galactic CR sources from theory and experimental data is summarized. In particular, the focus of this review lies on the search for photon and neutrino signals from the Galaxy and their theoretical interpretation in the context of the quest for the origin of high-energy cosmic rays. The use of multiwavelength data, from radio to TeV energies, as well as the option of coincident observations of different wavelength bands in order to pin-point the sources of Galactic CRs are discussed. Finally, the objectives for the field of astroparticles to reach the goal of unambiguously identifying Galactic cosmic ray sources within the next decades are presented.