Ultra-slow, ∼0.1-Hz variations in the oxygenation level of brain blood are widely used as an fMRI-based surrogate of “resting-state” neuronal activity. The temporal correlations among these fluctuations across the brain are interpreted as “functional connections” for maps and neurological diagnostics. Ultra-slow variations in oxygenation follow a cascade. First, they closely track changes in arteriole diameter. Second, interpretable functional connections arise when the ultra-slow changes in amplitude of γ-band neuronal oscillations, which are shared across even far-flung but synaptically connected brain regions, entrain the ∼0.1-Hz vasomotor oscillation in diameter of local arterioles. Significant confounds to estimates of functional connectivity arise from residual vasomotor activity as well as arteriole dynamics driven by self-generated movements and subcortical common modulatory inputs. Last, methodological limitations of fMRI can lead to spurious functional connections. The neuronal generator of ultra-slow variations in γ-band amplitude, including that associated with self-generated movements, remains an open issue.