Résumé : Identifying what makes up the Dark Matter is a long-standing problem to which the abundance of gravitational and cosmological evidence fails to answer. Indirect detection techniques have the aim to unveil the nature of Dark Matter by catching and identifying the products of potential decays and/or annihilations. The work exposed in this thesis is in line with this strategy and has for common thread the quest for line(-like) features in the extraterrestrial fluxes of gamma-rays and neutrinos. The motivation behind this specific interest is that, due to the absence of astrophysical counterparts beyond the GeV scale, these features constitute the ultimate probes (also called “smoking guns”) of the existence of Dark Matter.The thesis is organized in three Parts, the first of which is an introduction to the different facets of the Dark Matter conundrum and why it is not a trivial issue. The works involving gamma-ray line considerations are gathered in Part II, and those exclusively focusing on neutrino lines in Part III.Part II focuses on the effective field theory of Dark Matter decay, first in the context of millicharged particles decaying to gamma-ray lines, and then in the context of (neutral and millicharged) Dark Matter decays involving the simultaneous emission of gamma-ray and neutrino lines. In both cases, the simultaneous emission of cosmic rays is unavoidable and the decays are constrained in a multi-messenger fashion. The complementarity of the results obtained is used to derive model-independent constraints on the Dark Matter lifetime, and shows the possibility to exclude or distinguishsome specific scenarios on the basis of an explicit experimental conjecture.After an introduction to the neutrino detection principles and to the operation of the IceCube detector, Part III focuses on two careful searches for spectral features in the neutrino spectrum. The main goal behind these analyses, conducted in two different regions of the energy spectrum but using the same likelihood ratio procedure, is to popularize dedicated energy distribution studies by showing their ability to reach sensitivity levels comparable to—sometimes even going beyond—those obtained with angular distribution studies or even in the context of gamma-ray line searches.