We present atmospheric baseline growth rates from the 1970s to the present for the long-lived, strongly infrared-absorbing perfluorocarbons (PFCs) tetrafluoromethane (CF4), hexafluoroethane (C2F6), and octafluoropropane (C3F8) in both hemispheres, measured with improved accuracies (similar to 1-2%) and precisions (<0.3%, or <0.2 ppt (parts per trillion dry air mole fraction), for CF4; <1.5%, or <0.06 ppt, for C2F6; <4.5%, or <0.02 ppt, for C3F8) within the Advanced Global Atmospheric Gases Experiment (AGAGE). Pre-industrial background values of 34.7 +/- 0.2 ppt CF4 and 0.1 +/- 0.02 ppt C2F6 were measured in air extracted from Greenland ice and Antarctic firn. Anthropogenic sources are thought to be primary aluminum production (CF4, C2F6, C3F8), semiconductor production (C2F6, CF4, C3F8) and refrigeration use (C3F8). Global emissions calculated with the AGAGE 2-D 12-box model are significantly higher than most previous emission estimates. The sum of CF4 and C2F6 emissions estimated from aluminum production and non-metal production are lower than observed global top-down emissions, with gaps of similar to 6 Gg/yr CF4 in recent years. The significant discrepancies between previous CF4, C2F6, and C3F8 emission estimates and observed global top-down emissions estimated from AGAGE measurements emphasize the need for more accurate, transparent, and complete emission reporting, and for verification with atmospheric measurements to assess the emission sources of these long-lived and potent greenhouse gases, which alter the radiative budget of the atmosphere, essentially permanently, once emitted.