Being a subject I am interested in but know little about, a little while ago I made some notes on hemispheric specialisation. It's by no means a comprehensive overview, but I think there are some intriguing points, so I post it here in the hope that it interests someone else.
That hemispheric specialization exists to some extent is widely accepted: there are two theories regarding the reasons why this emerged . First is the theory that over the course of evolution, nervous system sizes increased. This led to the need for more efficient use of the intracranial space, which led to the folding of the cerebral cortex, and, it is hypothesized, hemispheric specialization. Second is the theory that with increases in brain sizes came increased distances over which neural signals had to travel, leading to an increased amount of time required for transmission. As there is no evidence for the increase in speed of transmission, the net logical step is the shortening of the distances involved. This is proposed to be the driving force behind hemispheric specialization: the need for reduction in distance of transmission. In apparent support for this view is the observation that larger brains have, proportionally speaking, a smaller corpus callosum, resulting in fewer trans-hemispheric connections and thus increased specialization.
With regard to the nature of the hemispheric specialization itself, there seem to be two competing views: material-specific and process-specific specialization. The material-specific view is that each cerebral cortex hemisphere is specialized for a particular type of information . For example, a study by Kelley et al on the dorsal frontal cortex found left sided activation for word encoding (verbal), right sided activation for face encoding (non-verbal), and bilateral activation for object encoding (both verbal and non-verbal) . Similar results found for the medial temporal lobe. This was replicated by , who found that interference with the right dorsolateral prefrontal cortex caused disruption to the encoding of patterned stimuli (hence non-verbal). A possible explanation for this type of specialization comes from Josse and Tzourio-Mazoyer . It is asserted that the left auditory cortex is specialized for temporal (i.e. time based) analysis, whilst the right auditory cortex is specialized for spectral (i.e. frequency based) analysis, which it is argued could explain the specialization of the left hemisphere for language, where the temporal content of speech is more important, and the specialization of the right hemisphere for music, where the spectral nature of the auditory information is more important.
This last point, concerning the specialization of the right hemisphere for music, has been contested by  for example, who emphasized the bilateral nature of activations due to various musical semantic and episodic tasks. More importantly here however, is their overall finding that there is generally a functional specialization of the left hemisphere for semantic memory tasks, and of the right hemisphere for episodic memory tasks. These findings were consistent with the HERA model of frontal cortex lateralization developed by Tulving et al in 1994 . This model is a process-specific specialization view with the same views as those expressed by  with regard to hemispheric specialization.
As I said, a very brief overview. Hopefully, people who know more can fill in some of the gaps by leaving some comments. Thanks!
 Josse, G.; Tzourio-Mazoyer, N. (2004), Hemispheric specialization for language, Brain Research Reviews, 44, pp1-12
 Glosser, G. et al (1998), Differential lateralization of memory discrimination and response bias in temporal lobe epilepsy patients, Journal of the International Neuropsychological Society, 4, pp502-511 (Abstract)
 Kelley, W.M. et al (1998), Hemispheric specialization in human dorsal frontal cortex and medial temporal lobe for verbal and nonverbal memory encoding, Neuron, 20, pp927-936
 Epstein, C. et al (2002), Asymmetries of prefrontal cortex in human episodic memory: effects of transcranial magnetic stimulation on learning abstract patterns, Neuroscience Letters, 30, pp5-8
 Tulving, E. et al (1994), Hemispheric encoding/retrieval asymmetry in episodic memory: positron emission tomography findings, Proceedings of the National Academy of Science USA, 91, pp2016-2020