Current understanding of the cortical mechanisms of speech perception and production stems mostly from studies that focus on single words or sentences. However, it has been suggested that processing of real-life connected speech may rely on additional cortical mechanisms. In the present study, we examined the neural substrates of natural speech production and perception with magnetoencephalography by modulating three central features related to speech: amount of linguistic content, speaking rate and social relevance. The amount of linguistic content was modulated by contrasting natural speech production and perception to speech-like non-linguistic tasks. Meaningful speech was produced and perceived at three speaking rates: normal, slow and fast. Social relevance was probed by having participants attend to speech produced by themselves and an unknown person. These speech-related features were each associated with distinct spatiospectral modulation patterns that involved cortical regions in both hemispheres. Natural speech processing markedly engaged the right hemisphere in addition to the left. In particular, the right temporo-parietal junction, previously linked to attentional processes and social cognition, was highlighted in the task modulations. The present findings suggest that its functional role extends to active generation and perception of meaningful, socially relevant speech.