Understanding spoken language requires the rapid transition from perceptual processing of the auditory input through a variety of cognitive processes involved in constructing the mental representation of the message that the speaker is intending to convey. Listeners carry out these complex processes very rapidly and accurately as they hear each word incrementally unfolding in a sentence. However, little is known about the specific spatiotemporal patterning of this wide range of incremental processing operations that underpin the dynamic transitions from the speech input to the development of a meaning interpretation of an utterance. This thesis aims to address this set of issues by investigating the spatiotemporal dynamics of brain activity as spoken sentences unfold over time in order to illuminate the neurocomputational properties of the human language processing system and determine how the representation of a spoken sentence develops incrementally as each upcoming word is heard. Using a novel application of multidimensional probabilistic modelling combined with models from computational linguistics, I developed models of a variety of computational processes associated with accessing and processing the syntactic and semantic properties of sentences and tested these models at various points as sentences unfolded over time. Since a wide range of incremental processes occur very rapidly during speech comprehension, it is crucial to keep track of the temporal dynamics of the neural computations involved. To do this, I used combined electroencephalography and magnetoencephalography (EMEG) to record neural activity with millisecond resolution and analyzed the recordings in source space using univariate and/or multivariate approaches. The results confirm the value of this combination of methods in examining the properties of incremental speech processing. My findings corroborate the predictive nature of human speech comprehension and demonstrate that the effects of early semantic constraint are not dependent on explicit syntactic knowledge.