|Brain: Corticospinal tract|
Deep dissection of brain-stem. Lateral view. ("pyramidal tract" visible in red, and "pyramidal decussation" labeled at lower right.)
Spinal cord tracts, with pyramidal tracts labeled at upper left
The pyramidal tracts refer to both the corticospinal and corticobulbar tracts. These are aggregations of upper motor neuron nerve fibres that travel from the cerebral cortex and terminate either in the brainstem (corticobulbar) or spinal cord (corticospinal) and are involved in control of motor functions of the body.
The corticobulbar tract conducts impulses from the brain to the cranial nerves. These nerves control the muscles of the face and neck and are involved in facial expression, mastication, swallowing, and other functions.
The corticospinal tract conducts impulses from the brain to the spinal cord. It is made up of a lateral and anterior tract. The corticospinal tract is involved in voluntary movement. The majority fibres of the corticospinal tract cross over in the medulla, resulting in muscles being controlled by the opposite side of the brain. The corticospinal tract also contains betz cells (the largest pyramidal cells), which are not found in any other region of the body.
The myelination of the pyramidal fibres is incomplete at birth and gradually progresses in caudo-cranial direction and thereby progressively gaining functionality. Most of the myelination is complete by two years of age and thereafter it progresses very slowly in cranio-caudal direction upto the age of twelve years of age.
The pyramidal tracts refer to upper motor neurons that originate in the cerebral cortex and terminate in the spinal cord (corticospinal) or brainstem (corticobulbar). Nerves emerge in the cerebral cortex, pass down and may cross sides in the medulla, and travel as part of the spinal cord until they synapse with interneurons in the middle part of the spinal cord, known as grey matter.
There is some variation in terminology. The pyramidal tracts definitively encompass the corticospinal tracts. Many, but not all authors also consider the tracts to include the corticobulbar tracts.
Nerve fibres in the corticospinal tract originate from from pyramidal cells in layer V of the cerebral cortex. Fibres arise from the primary motor cortex (about 30%), supplementary motor area and the premotor cortex (together also about 30%), and the somatosensory cortex, parietal lobe, and cingulate gyrus supplies the rest. The cells have their bodies in the cerebral cortex, and the axons form the bulk of the pyramidal tracts.  The nerve axons travel from the cortex through the posterior limb of internal capsule, through the cerebral peduncle and into the brainstem and anterior medulla. Here they form two prominences called the pyramids of the medulla. Below the prominences, the majority of axons cross over to the opposite side from which they originated. The axons that cross over move to the outer part of the medulla and form the lateral corticospinal tract, whereas the fibres that do not form remain form the anterior corticospinal tract  About 80% of axons cross over and form the lateral corticospinal tract; 10% do not cross over and join the tract, and 10% of fibres travel in the anterior corticospinal tract.
The nerve axons travelling down the tract are referred to as upper motor neurons. These axons travel down the tracts in the white matter of the spinal cord until they reach the vertebral level of the muscle that they will innervate. At this point, the axons synapse with lower motor neurons. The majority of axons do not directly synapse with lower motor neurons, but instead synapse with an interneuron that then synapses with a lower motor neuron. This generally occurs in the anterior horn of the spinal cord. Nerve axons of the lateral corticospinal tract that did not cross over in the medulla do so at the level of the spinal cord they terminate in. 
The majority of nerve axons are small (<4μm) in diameter. About 3% of nerve axons have a much larger diameter (16μm) and arise from Betz cells, mostly in the leg area of the primary motor cortex. These cells are notable because of their rapid conduction rate, over 70m/sec, the fastest conduction of any signals from the brain to the spinal cord. 
Fibres from the wikt:ventral motor cortex travel with the corticospinal tract through the internal capsule, but terminate in a number of locations in the midbrain (cortico-mesencephalic tract), pons (Corticopontine tract), and medulla oblongata (cortico-bulbar tract).  The upper motor neurons of the corticobulbar tract synapse with interneurons or directly with the lower motor neurons located in the motor cranial nerve nuclei, namely oculomotor, trochlear, motor nucleus of the trigeminal nerve, abducens, facial nerve and accessory and in the nucleus ambiguus to the hypoglossal, vaguss and accessory nerves.  These nuclei are supplied by nerves from both sides of the brain, with the exception of the parts of the facial nerve that control muscles of the lower face. These muscles are only innervated by nerves from the same side of the brain. 
The nerves within the corticospinal tract are involved in movement of muscles of the body. Because of the crossing-over of fibres, muscles are supplied by the side of the brain opposite to that of the muscle.  The nerves within the corticobulbar tract are involved in movement in muscles of the head. They are involved in swallowing, phonation, and movements of the tongue.  By virtue of involvment with the facial nerve, the corticobulbar tract is also responsible for transmitting facial expression.  With the exception of lower muscles of facial expression, all functions of the corticobulbar tract involve inputs from both sides of the brain. 
The term extrapyramidal motor system is used to refer to tracts within the spinal cord involved in voluntary movement but not part of the pyramidal tracts.  Their functions include voluntary movement, control posture and muscle tone.
If fibres of the corticospinal tracts are damaged anywhere along their course from the cerebral cortex to the lower end of the spinal cord, this will give rise to an upper motor neuron syndrome. A few days after the injury to the upper motor neurons, a pattern of motor signs and symptoms appears, including spasticity, hyperactive reflexes, a loss of the ability to perform fine movements, and an extensor plantar response known as the Babinski sign. Symptoms generally occur alongside other sensory problems. Causes of damage may include masses such as strokes, subdural hemorrhage, absesses and tumours, inflammation such as meningitis and multiple sclerosis, and trauma to the spinal cord, including from slipped discs.
If the corticobulbar tract is damaged on only one side, then only the lower face will be affected, however if there is involvement of both the left and right tracts, then the result is pseudobulbar palsy. This causes difficulties swallowing, speaking, and emotional lability. 
Diagram of the principal fasciculi of the spinal cord, from Gray's anatomy
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