When faced with situations where many people talk at once, individuals can employ different listening strategies to deal with the cacophony of speech sounds and to achieve different goals. In this fMRI study, we investigated how the pattern of neural activity is affected by the type of attention applied to speech in a simulated “cocktail party.” Specifically, we compared brain activation patterns when listeners “attended selectively” to only one speaker and ignored all others, versus when they “distributed their attention” and followed several concurrent speakers. Conjunction analysis revealed a highly overlapping network of regions activated for both types of attention, including auditory association cortex (bilateral STG/STS) and frontoparietal regions related to speech processing and attention (bilateral IFG/insula, right MFG, left IPS). Activity within nodes of this network, though, was modulated by the type of attention required as well as the number of competing speakers. Auditory and speech-processing regions exhibited higher activity during distributed attention, whereas frontoparietal regions were activated more strongly during selective attention. These results suggest a common “attention to speech” network, which provides the computational infrastructure to deal effectively with multi- speaker input, but with sufficient flexibility to implement different prioritization strategies and to adapt to different listener goals.