The authors introduce a flexible and robust simulation-based framework to infer demographic parameters from the site frequency spectrum (SFS) computed on large genomic datasets. Their composite-likelihood approach allows for the study of evolutionary models of arbitrary complexity, which cannot be handled by other current likelihood-based methods. For simple scenarios, their method compares favorably in terms of accuracy and speed with $\hat{c}a\hat{c}i$, a widely used diffusion-based method, while showing better convergence properties for complex models. The authors apply their methodology to non-coding genomic SNP data from four human populations, inferring their demographic history by comparing neutral evolutionary models of increasing complexity, including unsampled populations. They also extend their framework to the inference of demographic parameters from SNP chips with known ascertainment bias, such as those recently released by Affymetrix for studying human origins. The framework can correctly infer parameters of complex models, including the divergence of several populations, bottlenecks, and migration. They apply this approach to reconstruct the African demography using two distinct ascertained human SNP panels, studying two evolutionary models. The two SNP panels yield very similar estimates and confidence intervals, suggesting an ancient divergence (>110 Ky) between Yoruba and San populations. The methodology is well-suited for studying complex scenarios from large genomic datasets.The authors introduce a flexible and robust simulation-based framework to infer demographic parameters from the site frequency spectrum (SFS) computed on large genomic datasets. Their composite-likelihood approach allows for the study of evolutionary models of arbitrary complexity, which cannot be handled by other current likelihood-based methods. For simple scenarios, their method compares favorably in terms of accuracy and speed with $\hat{c}a\hat{c}i$, a widely used diffusion-based method, while showing better convergence properties for complex models. The authors apply their methodology to non-coding genomic SNP data from four human populations, inferring their demographic history by comparing neutral evolutionary models of increasing complexity, including unsampled populations. They also extend their framework to the inference of demographic parameters from SNP chips with known ascertainment bias, such as those recently released by Affymetrix for studying human origins. The framework can correctly infer parameters of complex models, including the divergence of several populations, bottlenecks, and migration. They apply this approach to reconstruct the African demography using two distinct ascertained human SNP panels, studying two evolutionary models. The two SNP panels yield very similar estimates and confidence intervals, suggesting an ancient divergence (>110 Ky) between Yoruba and San populations. The methodology is well-suited for studying complex scenarios from large genomic datasets.