Objective. Music and speech are complex signals containing regularities in how they unfold in time. Similarities between music and speech/language in terms of their auditory features, rhythmic structure, and hierarchical structure have led to a large body of literature suggesting connections between the two domains. However, the precise underlying mechanisms behind this connection remain to be elucidated. Method. In this theoretical review paper, we synthesize previous research and present a framework of potentially shared neural mechanisms for music and speech rhythm processing. We outline structural similarities of rhythmic signals in music and speech, synthesize prominent music and speech rhythm theories, discuss impaired timing in developmental speech and language disorders, and discuss music rhythm training as an additional, potentially effective therapeutic tool to enhance speech/language processing in these disorders. Results. We propose the processing rhythm in speech and music (PRISM) framework, which outlines three underlying mechanisms that appear to be shared across music and speech/language processing: precise auditory processing, synchronization/entrainment of neural oscillations to external stimuli, and sensorimotor coupling. The goal of this framework is to inform directions for future research that integrate cognitive and biological evidence for relationships between rhythm processing in music and speech. Conclusion. The current framework can be used as a basis to investigate potential links between observed timing deficits in developmental disorders, impairments in the proposed mechanisms, and pathology-specific deficits which can be targeted in treatment and training supporting speech therapy outcomes. On these grounds, we propose future research directions and discuss implications of our framework.