The cerebrum is responsible for olfaction, or the sense of smell. The other portions of the brain listed are responsible mainly for balance (cerebellum) and primitive functions such as respiratory and heart rate (brain stem).
After odorant molecules (scents) become stuck in and dissolve in the mucus of the nasal cavity, they lead to action potentials or messages being sent to the two olfactory nerves. The message then goes to several places in the cerebrum once it reaches the brain.
1. The primary olfactory cortex- This is where information about the scent is first processed. The primary olfactory cortex is located in a part of the brain known as the insula, a region of the cerebral cortex that can be seen only when the frontal/parietal lobes are pulled away from the temporal lobe at the lateral sulcus. Diseases such as Alzheimer's lead to destruction of this region of the brain, explaining why inability to detect odor can be an early warning sign of such diseases.
2. The prefrontal cortex (the frontal lobe)- The message is also sent here. The frontal lobe allows additional processing in addition to allowing one to discriminate between different scents so that the odor being detected can be identified.
3. The limbic system- Components of the limbic system surround the thalamus in the central part of the brain. The limbic system is generally associated with emotion and memory. When you think of a specific memory (for example, going to visit your grandma) when you smell a specific scent (apple pie for example), it is because information regarding the odor is sent to this region of the brain.