In 2373, Voyager reached the edge of Swarm space. The first contact came when a Swarm vessel encountered one of Voyager's shuttles. The encounter did not go well; two Swarm members beamed aboard and fired on the crew without warning using a neuro-electric weapon. Which inflicted severe trauma on the nervous system. Fortunately the crewmembers were quickly rescued, and Voyager's EMH was able to successfully treat the damage. 
A mysterious species, the Swarm were largely an unknown quantity to Neelix, the ship's Delta Quadrant expert. Most ships which entered their territory did not return, or returned but with everybody aboard dead. Nobody knew the real name of the species, their numbers, or any details of their culture. The only contact the Swarm had with other species was a single repeating message which even the universal translator could not interpret. 
It would take Voyager some fifteen months to travel around Swarm space even at maximum warp speeds, but by choosing their course carefully the ship would be in Swarm space for only four days. The Swarm maintained a network of interlaced tachyon beams to detect ships crossing their borders; by adjusting the shields to refract the beams, the ship was able to pass through undetected. As they made the attempt, the ship detected a vast fleet of small Swarm vessels in their space, all lying dormant with no weapons or propulsion powered. Undeterred, Captain Janeway ordered the ship through Swarm space in violation of Starfleet regulations. 
Unfortunately, things soon began to go wrong. Voyager, already limited to warp 9.75  from her top speed of 9.975 , was further slowed by a resonance particle wave which dampened the warp field. Then they encountered a disabled freighter which had been very badly damaged. Recovering a survivor, they found that the Swarm fleet had attacked him. They clamped onto his ship, draining the energy from it and sending boarding parties who killed used neuro-electric weapons to kill the crew. Despite the best efforts of Voyager's EMH, the man was too badly wounded to survive. 
Worse was to follow; an active Swarm vessel was still attached to Voyager, and fired a polaron beam at the ship which changed the shield polarity and made it clearly visible to every other Swarm ship in the vicinity. The large fleet powered up and pursued Voyager, using an interferometric pulse which modulated in opposition to the Starship's shield frequencies, cancelling them out and dismantling the shields completely. The same pulse reflected phaser fire directly back at Voyager, and without shields use of photon torpedoes was impossible. 
The Swarm vessels clamped onto Voyager's hull, draining the ship's systems and transporting boarding parties aboard. Fortunately Ensign Kim was able to analyse the interferometric pulse, discovering that it was an energy lattice which connected all the Swarm ships together. With a modification of the shields to resist the phaser reflection effect, Janeway was able to score a solid hit on one ship which in turn disabled the whole fleet via their connection. The Starship was able to escape the Swarm and proceed on course.