In this thesis we study axions, a byproduct of the Peccei-Quinn solution to the strong CP problem, which are also a viable candidate for the dark matter content of the Universe. In the first part of the thesis, we revisit the Dine-Fischler-Srednicki-Zhitnisky axion model in light of the recent Higgs LHC results and electroweak precision data. This model is an extension of the two-Higgs-doublet model incorporating a PQ symmetry which leads to a physically acceptable axion. For generic values of the couplings, the model reproduces the minimal Standard Model, with a massless axion and all the other degrees of freedom at a very high scale. However, in some scenarios, the extra Higgses could be relatively light. We use the oblique corrections, in particular $Deltarho$, to constrain the mass spectrum in this case. Finally, we also work out the non-linear parametrization of the DFSZ model in the generic case where all scalars except the lightest Higgs and the axion have masses at or beyond the TeV scale. In the second part, we study the relevance of a cold axion background (CAB) as a responsible for the dark matter in the Universe. We examine indirect consequences of its presence through its effects on photon and cosmic ray propagation. First, we study the axion-photon system under the joint influence of two backgrounds: an external magnetic field and a CAB. Their effect consists in producing a three-way mixing of the axion with the two polarizations of the photon. We determine the proper frequencies and eigenvectors as well as the corresponding photon ellipticity and induced rotation of the polarization plane that depend both on the magnetic field and the local density of axions. We also comment on the possibility that some of the predicted effects could be measured in optical table-top experiments. Then, we consider the case in which no magnetic field is present. Here, circularly polarized photons are energy eigenstates, with a modified dispersion relation. This enables the emission of a photon by a charged particle, such as a cosmic ray, which is forbidden in regular QED due to energy-momentum conservation. We study the energy loss of a cosmic ray due to this process and compute the energy flux of photons emitted in this way, which depends on the cosmic ray spectrum.