Epidemiology and public health planning will increasingly rely on the analysis of genetic sequence data. The ongoing influenza A/H1N1 pandemic may represent a tipping point in this trend, with A/H1N1 being the first human pathogen routinely genotyped from the beginning of its spread. To take full advantage of this genetic information, we introduce a novel method to reconstruct the spatiotemporal dynamics of outbreaks from sequence data. The approach is based on a new paradigm were ancestries are inferred directly rather than through the reconstruction of most recent common ancestors (MRCAs) as in phylogenetics. Using 279 A/H1N1 hemagglutinin (HA) sequences, we confirm the emergence of the 2009 flu pandemic in Mexico. The virus initially spread to the US, and then to the rest of the world with both Mexico and the US acting as the main sources. While compatible with current epidemiological understanding of the 2009 H1N1 pandemic, our results provide a much finer picture of the spatiotemporal dynamics. The results also highlight how much additional epidemiological information can be gathered from genetic monitoring of a disease outbreak.