The right cerebral hemisphere is one of the two longitudinal halves into which the cerebrum is divided. Like the left, it is divided into four lobes: the frontal, temporal, parietal, and occipital. The right hemisphere motor strip controls the muscular movement of the left side of the body; that is to say that left-handed people are lateralized towards the right hemisphere.
The right cerebral hemisphere is connected to the left hemisphere through the corpus callosum, which is a band of white matter composed of myelinated fibers. The right hemisphere is linked to the basal ganglia and thalamus through myelinated axons which go from its frontal lobe to these regions.
The right cerebral hemisphere functions differently from the left, as it seems to have a complete different way of processing the data, or different approach to reality. It is wholistic, which means that the right hemisphere does not analyze incoming information, breaking it into parts, but synthesize it into one indivisible whole. It is also intuitive and imaginative.
The right cerebral hemisphere; external, lateral side. You can see the brainstem and the cerebellum below it.