The Fenna-Matthews-Olson (FMO) photosynthetic complex found in green sulfur bacteria has over the last decades been one of the favorite "model" systems for biological energy transfer. However, even after 40 years of studies, quantitative knowledge about its energy-transfer properties is limited. Here, two-dimensional electronic spectroscopy with full polarization control is used to provide an accurate description of the electronic structure and population dynamics in the complex. The sensitivity of the technique has further allowed us to spectroscopically identify the eighth bacterio-chlorophyll molecule recently discovered in the crystal structure. The time evolution of the spectral structure, covering time scales from tens of femtoseconds up to a nanosecond, reflects the energy flow in FMO and enables us to extract an unambiguous energy-transfer scheme.