The dual stream language processing models (dorsal and ventral) have replaced the historic model that only included the Broca's and Wernicke's areas and the arcuate fasciculus 1.
Function
The dorsal stream is responsible for phonological processing and language production (sound/sign to action). The ventral stream is responsible for orthographic and semantic processing (sound/sign to meaning). The two pathways overlap both in anatomical representations and function 1-3.
Relation
The ventral pathway is active in both cerebral hemispheres during visual, auditory and possibly tactile language input; the dorsal pathway, on the other hand, is specialized in speech output in the dominant hemisphere 1,2.
The white matter tracts play a crucial role in language processing and oftentimes damage to these structures results in a permanent speech disorder. However, because of neuroplasticity the function of a damaged cortical area is, at least partially, recovered by its neighbors 3.