Background and aims: The analysis of large-scale genetic data from thousands of individuals has revealed the fact that subtle population genetic structure can be detected at levels that were previously unimaginable. Using the Human Genome Diversity Panel as reference (51 populations - 650,000 SNPs), this works describes a systematic evaluation of the resolution that can be achieved for the inference of genetic ancestry, even when small panels of genetic markers are used. Methods and results: A comprehensive investigation of human population structure around the world is undertaken by leveraging the power of Principal Components Analysis (PCA). The problem is dissected into hierarchical steps and a decision tree for the prediction of individual ancestry is proposed. A complete leave-one-out validation experiment demonstrates that, using all available SNPs, assignment of individuals to their self-reported populations of origin is essentially perfect. Ancestry informative genetic markers are selected using two different metrics (In and correlation with PCA scores). A thorough cross-validation experiment indicates that, in most cases here, the number of SNPs needed for ancestry inference can be successfully reduced to less than 0.1% of the original 650,000 while retaining close to 100% accuracy. This reduction can be achieved using a novel clustering-based redundancy removal algorithm that is also introduced here. Finally, the applicability of our suggested SNP panels is tested on HapMap Phase 3 populations. Conclusion: The proposed methods and ancestry informative marker panels, in combination with the increasingly more comprehensive databases of human genetic variation, open new horizons in a variety of fields, ranging from the study of human evolution and population history, to medical genetics and forensics.