Humans are a highly mobile species that has colonized the entire globe in a few tens of thousands of years after it went out of Africa. There are still many unknowns about the routes followed by our ancestors during this expansion process, which has been influenced by various environmental, biological, and cultural factors, but these migrations have contributed to shape the genetic diversity of our species. A powerful approach to study the consequences of human dispersal on our genome is the modelling of complex evolutionary scenarios via computer simulation. In this chapter, we present three types of approaches used to simulate human dispersal in a geographic landscape. We focus on a spatially explicit method, simulating the demographic and migratory dynamic of populations forward in time and their resulting genetic diversity backward in time using the coalescent. We describe this approach and illustrate its interest with two important results: the process of gene surfing during population expansion and the genetic consequences of hybridization during species expansions. We show that a relatively simple scenario of global expansion of Homo sapiens from Africa, with rare hybridization events with archaic humans, such as Neanderthals or Denisovans, over a large geographic area reasonably explains the introgression pattern of archaic DNA in the genome of our species.