The energy lifeforms called "wisps" by the crew of Enterprise NX-01 originated as corporeal lifeforms of "substance" that evolved into a form of non-corporeal, massless, "perceptive energy," that existed and traveled through subspace. In their non-corporeal form, they contained no elements that could be identified by mid-22nd century Starfleet sensors.
Inside, the wisps flew freely in the ship's atmosphere, which consisted of helium with traces of xenon. Upon their first encounter with Humans, the wisps converted their atmosphere to one of nitrogen and oxygen. Shortly thereafter, they briefly inhabited Charles Tucker, before slowly taking over crew members, one by one, aboard Enterprise. Based on Tucker's experience, the wisps could swap places with a body's owner, who then spent time as a similar, but yellow-in-color wisp-creature. While they were in this state, the Humans were immersed in realistic hallucinations.
After having released Enterprise from their ship, the wisps traveled briefly through space and began entering Enterprise through the hull. First contact was then made through Tucker, who explained to Captain Archer that they were explorers who wished to explore the corporeal existence of their ancestors.
Once a number of crew members were taken over by the wisps, Phlox and T'Pol determined that those in the possessed state were characterized by elevated acetylcholine levels in the autonomic nervous system.
Eventually, and by accident, it was discovered that the wisps were unable to penetrate the osmium alloy of the hatchway into Enterprise's catwalk. As a result, the crew took refuge in the catwalk while they attempted to formulate a means to defeat the invaders.
When the wisps attempted to enter T'Pol, she was able to repel them with her mental discipline, at which point she discovered that they were lying, and were intending to take over the ship, as their own ship was breaking down and they possessed no way to repair it.
Finally, it was discovered that the "wisps" could be expelled by suffocating the Human hosts with carbon dioxide. Phlox flooded the ship with CO2 and freed all the crew of the wisps' influence. Enterprise quickly pulled away from their ship and destroyed it by firing two spatial torpedoes into the interior of the ship. (ENT: "The Crossing")