Dark matter (DM) is one of the biggest mysteries in physics, a non-baryonic matter that accounts for ∼ 85% of all matter in the Universe. It plays a vital role in the formation and evolution of large-scale and galactic structures, yet its nature still remains unknown. Many DM candidates have be theorised, most notably the WIMPs, however without a confirmed detection numerous questions remain. Definitive evidence for the existence of WIMPs, or of any other DM candidates, is actively sought via both direct and indirect detection experiments. This thesis explores the effect of baryons and the uncertainties associated with direct and indirect DM detection using ARTEMIS, a new suite of high- resolution cosmological hydrodynamic simulations of Milky Way-like galaxies, to aid identification of DM. I begin by investigating the uncertainties associated with DM direct detection experi- ments, which aim to place constraints on the DM–nucleon scattering cross-section and the DM particle mass. These constraints depend sensitively on the assumed local DM density, the DM velocity distribution function, and several particle physics parameters. While astrophysical observations can measure the local DM density relatively accu- rately, the DM velocity distribution function is less well constrained. Using a sample of 42 Milky Way-mass halos from ARTEMIS, I explore the spatial and kinematical distributions of the DM in the simulated solar neighbourhoods, and study how these quantities are influenced by DM substructure, baryons, the presence of dark discs, as well as general halo-to-halo scatter (cosmic variance). I investigate also the accuracy of the Maxwellian approach for modelling velocity distribution functions in the standard halo model and find that this accuracy is hampered by significant halo-to-halo scatter in the (simulated) velocity functions. Allowing for this scatter in the computation of the iii DM detection limits in the standard halo model methodology leads to a significant scat- ter about the exclusion limit that is typically quoted. The Maxwellian approximation works relatively well for our simulations that include the baryons, but it is less accurate for collisionless (DM-only) simulations. Given the significant halo-to-halo scatter in the quantities relevant for DM direct detection, it is recommended that this source of uncertainty is propagated through in order to derive conservative DM detection limits. Using the ARTEMIS simulations, I then examine the prospects of indirect DM detec- tion in the Milky Way with the upcoming Cherenkov Telescope Array (CTA) using the specific instrumental sensitivity of this facility. I investigate the baryonic effects in the γ-ray luminosities and fluxes resulted from the DM annihilation in both central halos and substructure. The unresolved substructure in the simulations is taken into account via the commonly used ‘boost’ factor. However, I find that the boost factor depends not only on the cut-off mass value but, importantly, also on the assumed c−M relation which is used to determine the concentration of the subhalos. The simulations show that the DM annihilation luminosities and fluxes of the host halos are higher for the halos containing baryons. This is due to the higher densities and concentrations of these halos as a result of adiabatic contraction in the presence of baryons, with the DM subhalos less affected. Using these results, I investigated whether a nominal 50-hour observation with CTA would be sensitive enough to detect an annihilation signal from the central Milky Way DM halo and nearby subhalos. I find that the signal from main halos via either bb, tt or τ+τ− channels would be detectable, at energies ∼ 20 GeV −1 TeV. For CTA to detect an annihilation signal from subhalos their individual contributions must be summed. In that case, a possible detection from substructure can be at ener- gies ∼ 200 − 700 GeV via the τ+τ− annihilation channel. One of the largest sources of uncertainty in the differential γ-ray flux comes from the assumed c−M relation in calculating boost factors, which can lead to changes in fluxes by up to a factor of ∼ 10. The results show that predictions for direct and indirect detection experiments need to carefully consider the associated astrophysical uncertainties. Also, the impact of bary- onic physics on the DM in halos and subhalos is significant, emphasising the importance of using hydrodynamic simulations for making predictions for the detectability of DM