Species generally undergo a complex demographic history, consisting, in particular, of multiple changes in population size. Genome-­wide sequencing data are potentially highly informative for reconstructing this demographic history. A crucial point is to extract the relevant information from these very large datasets. Here we designed an approach for inferring past demographic events from a moderate number of fully sequenced genomes. Our new approach uses Approximate Bayesian Computation (ABC), a simulation-­based statistical framework that allows (i) identifying the best demographic scenario among several competing scenarios, and (ii) estimating the best-­fitting parameters under the chosen scenario. ABC relies on the computation of summary statistics. Using a cross-­validation approach, we showed that statistics such as the lengths of haplotypes shared between individuals, or the decay of linkage disequilibrium with distance, can be combined with classical statistics (eg heterozygosity, Tajima's D) to accurately infer complex demographic scenarios including bottlenecks and expansion periods. We also demonstrated the importance of simultaneously estimating the genotyping error rate. Applying our method on genome-­wide human-­sequence databases, we finally showed that a model consisting in a bottleneck followed by a Paleolithic and a Neolithic expansion was the most relevant for Eurasian populations.