Abstract: The most widespread measures of human brain activity are the blood oxygen level dependent (BOLD) signal and surface field potential. Prior studies report a variety of relationships between these signals. To develop an understanding of how to interpret these signals and the relationship between them, we developed a model of (a) neuronal population responses, and (b) transformations from neuronal responses into the fMRI BOLD signal and electrocorticographic (ECoG) field potential. Rather than seeking a transformation between the two measures directly, this approach interprets each measure with respect to the underlying neuronal population responses. This model accounts for the relationship between BOLD and ECoG data from human visual cortex in V1-V3, with the model predictions and data matching in three ways: Across stimuli, the BOLD amplitude and ECoG broadband power were positively correlated, the BOLD amplitude and alpha power (8-13 Hz) were negatively correlated, and the BOLD amplitude and narrowband gamma power (30-80 Hz) were uncorrelated. The two measures provide complementary information about human brain activity and we infer that features of the field potential that are uncorrelated with BOLD arise largely from changes in synchrony, rather than level, of neuronal activity.