All human cognition is controlled in a series of attentional episodes, breaking complex problems into simpler, more solvable sub-problems.  In human fMRI studies, a common or multiple-demand (MD) pattern of frontal and parietal activity is associated with diverse cognitive demands, and with standard tests of fluid intelligence.  Based on behavioural, neuropsychological, fMRI and single unit data, I suggest that the core function of MD cortex is to control complex cognition in a structured sequence of attentional episodes.  At the same time, I consider the complementary control functions of MD and “default mode” networks.