An intense debate animates the Earth Sciences community about the impact of the Glaciations on mountain ranges. Mountains develop their relief from the interaction of tectonics with climate through erosion. Erosion breaks rocks in the highland, and rivers and submarine gravity flows (turbidites) transfer the waste material to sedimentary basins. Erosion results from the action of rainfall, rivers or glaciers. Studies suggest that changes in the rainfall amplitude or seasonality, and changes in the extent of glaciers have triggered a worldwide and considerable increase of erosion rates for the last millions of years. However, this hypothesis is debated because past erosion rates are estimated with indirect approaches. Here, I focus on the Himalaya, the iconic mountain range at the convergence of the Indian and Eurasian plates. There, the highests summits and the deepest valleys on Earth grow. Landslides and glacial erosion supply one of the highest sedimentary fluxes to the oceans. To determine the past erosion rates, I measured the amount of the 10Be cosmogenic isotope accumulated in the quartz sediment. These isotopes are produced at Earth's surface by the interaction of cosmic rays with matter. Isotopes gradually accumulate in rocks close to the surface, depending on the elevation and the erosion rates. The isotopic concentration in sediment gives access to the average erosion rate of the source drainage basin. To determine the source of sediment and the deposition paleoenvironment, I performed supplementary measurements on Sr-Nd and C-O isotopes. I conducted my measurements on two sites. Site A consists in sandy turbidites sedimented on the deep sea floor of the Bengal Bay and collected by Expeditions 353 and 354 of the International Ocean Discovery Program. Site B consists in molasse sediment deposited at the front of the Himalaya, in the Siwalik Hills, within the Valmiki Wildlife Sanctuary in India. Site A integrates the erosion of the Ganga and Brahmaputra drainage basins, covering Central and Eastern Himalaya. Site B integrates the erosion of the Narayani-Gandak basin, covering Central Nepal. My results yield an unprecedented insight in the variation of erosion in a mountain range over the last seven million years. They imply that average erosion rates have been steady since at least three million years in the Himalaya, despite the variations in sediment transfer or the locus of erosion, and despite intense late Cenozoic Glaciations.