This dissertation is concerned with whether the sentence processor can compute plausible relations among a cluster of neighboring open class words without taking into account the relationships between these words as dictated by the structure of the sentence. It has been widely assumed that compositional semantics is built on top of syntactic structures (Heim & Kratzer, 1998; Pollard & Sag, 1994). This view has been challenged by recent electrophysiological findings (Kim and Osterhout, 2005; Kuperberg, 2007; van Herten et al., 2005, 2006) that appear to show that semantic composition can proceed independently of syntactic structure. This dissertation investigates whether the evidence for independent semantic composition is as strong and widespread as has been previously claimed. Recent studies have shown that sentences containing a semantically anomalous interpretation but an unambiguous, grammatical structure (e.g., The meal was devouring) elicit a P600 response, the component classically elicited by syntactic anomalies, rather than an N400, the component typically elicited by semantic anomalies (Kim and Osterhout, 2005). This has been interpreted as evidence that the processor analyzed meal as a good theme for devour, even though this interpretation is not supported by the sentential structure. This led to the claim that semantic composition can proceed independently of syntactic structure. Two event-related potentials (ERP) studies investigated whether the processor exploits prior structural biases and commitments to restrict semantic interpretations to those that are compatible with that expected structure. A further ERP study and a review of relevant studies reveal that in the majority of studies the P600 is not modulated by manipulations of thematic fit or semantic association between the open class words. We argue that a large number of studies that have been taken as evidence for an independent semantic processing stream can be explained as violations of the verb's requirement that its subject be agentive. A small number of studies in verb-final languages cannot be explained in this way, and may be evidence of independent semantic composition, although further experimental work is needed. We conclude that the evidence for independent semantic composition is not as extensive as was previously thought.