The corticospinal tract mostly contains motor axons. It actually consists of two separate tracts in the spinal cord: the lateral corticospinal tract and the anterior corticospinal tract. An understanding of these tracts leads to an understanding of why for the most part, one side of the body is controlled by the opposite side of the brain.
Also the corticobulbar tract is considered to be a pyramidal tract. The corticobulbar tract carries signals that control motor neurons located in cranial nerve brain nuclei rather than motor neurons located in the spinal cord.
The neurons of the pyramidal tracts are pyramidal neurons, but that is not how the pyramidal tract got its name, as most of the pyramidal neurons send their axons elsewhere. Instead, it got its name from the shape of the corticospinal axon tracts: when the pyramidal tract passes the medulla, it forms a dense bundle of nerve fibres that is shaped somewhat like a pyramid.
Whichever of these two tracts it travels in, a cortico-spinal axon will synapse with another neuron in the ventral horn. This ventral horn neuron is considered a second-order neuron in this pathway, but is not part of the corticospinal tract itself.
The motor fibers continue down into the brainstem. The bundle of corticospinal axons is visible as two column-like structures ("pyramids") on the ventral surface of medulla oblongata - this is where the name pyramidal tract comes from.
After the decussation, the axons travel down the spinal cord as the lateral corticospinal tract. Fibers that do not cross over in the medulla oblongata travel down the separate anterior corticospinal tract, and most of them cross over to the contralateral side in the spinal cord, shortly before reaching the lower motor neurons.
In the brain stem, the lower motor neurons are located in the motor cranial nerve nuclei (occulomotor, trochlear, motor nucleus of the trigeminal nerve, abducens, facial, accessory, hypoglossal). The lower motor neuron axons leave the brain stem via motor cranial nerves and the spinal cord via anterior roots of the spinal nerves respectively, end-up at the neuromuscular plate and provide motor innervation for voluntary muscles.