In the last few years, two paradigms underlying human evolution have crumbled. Modern humans have not totally replaced previous hominins without any admixture, and the expected signatures of adaptations to new environments are surprisingly lacking at the genomic level. Here we review current evidence about archaic admixture and lack of strong selective sweeps in humans. We underline the need to properly model differential admixture in various populations to correctly reconstruct past demography. We also stress the importance of taking into account the spatial dimension of human evolution, which proceeded by a series of range expansions that could have promoted both the introgression of archaic genes and background selection.