Understanding the nature of dark matter is one of the greatest challenges of modern physics. If dark matter is made of particles, we can hope to detect it, directly or indirectly, using Earth-based or spatial experiments. Make predictions for the outcome of these experiments, or interpret the results in case of a detection, requires a deep understanding of the structuring of dark matter in our Galaxy. Starting from particle physics and cosmological considerations, I built a dynamically constrained model of the Galactic dark halo including a detailed description of its inhomogeneities. The impact of these inhomogeneities on searches with cosmic rays is then analysed in details. I also study a method allowing to predict the phase-space distribution of dark matter particles, and discuss its possible application to dark matter searches. This method is then applied to searches with cosmic-ray electrons and positrons, and new very stringent constraints are obtained on microscopic models of dark matter.