(covers information from several alternate timelines)
The Krenim were a technologically-advanced humanoid species from the Delta Quadrant, first encountered by the Federation starship USS Voyager in 2374. The Krenim government was called the Krenim Imperium.
At 98% restoration, the Krenim Imperium of 2374 was composed of over two hundred star systems, nine hundred planets, and thousands of warp-capable vessels spread out over five thousand parsecs. (VOY: "Year of Hell")
In the Year of Hell, Voyager traversed Krenim space beginning on stardate 50973, enduring constant Krenim attacks. A large number of the crew was killed, including Captain Kathryn Janeway, B'Elanna Torres, and Joe Carey. During one of the Krenim attacks, Kes was exposed to chroniton radiation which leaked through the hull from a chroniton torpedo fragment. Much later in 2379, The Doctor's attempt to extend her short Ocampan life span using a bio-temporal chamber activated the dormant chronitons inside her body, causing her to travel randomly backwards in time to various points in her own life. The Doctor of 2373 was able to purge the chronitons using anti-chronitons, synchronizing Kes to the year 2373. While she was in 2373, Kes warned Janeway of the Krenim danger. (VOY: "Before and After")
According to the Krenim officer known as Annorax, their greatest adversary was a race known as the Rilnar. Unbeknownst to the Krenim, however, the Rilnar had introduced a crucial antibody into the Krenim genome which prevented certain diseases from affecting the Krenim. In at least one alternate timeline, Annorax wiped out the Rilnar civilization without realizing the existence of the antibody and an epidemic swept across the Krenim homeworld, killing fifty million people in the first year alone.
In a number of separate alternate timelines in 2374, Voyager attempted to enter Krenim territory. Initially, they encountered only a small, poorly armed Krenim ship. In this timeline, the region was dominated by the Zahl, who had ended the Krenim domination of the region a generation previously. This timeline was changed when the Krenim weapon ship erased the Zahl civilization, removing the entire species from history. In this new timeline, the Krenim Imperium was near the height of its power, and launched a series of devastating attacks on Voyager much like the "year of hell" of Kes's possible future.
Eventually, Voyager developed temporal shields to defend against the Krenim, which in turn perturbed the temporal calculations made by the weapon ship. Thus, the elimination of the Garenor species, intended to further restore the Imperium, instead created a third alternate timeline where the Krenim regressed to a pre-warp society. The temporal shields protected Voyager from the changes to the timeline, and its crew was able to see the changes the Krenim had made. (VOY: "Year of Hell")
Eventually, Voyager created an alliance with the Mawasi and the Nihydron in order to attack the weapon ship. The damage they dealt to the weapon ship caused it to erase itself from the timeline, undoing all of the damage it had done.
In this restored timeline, Voyager encountered a Krenim warship in 2374. Its commandant warned Captain Janeway that the region of space they were passing through was in dispute and that they should avoid it if possible. He wished them good journey and the two ships went their separate ways. (VOY: "Year of Hell, Part II")
In the computer game Star Trek Online, the Krenim have been specifically targeted by the Vaadwaur (under the direction of the Iconians) and nearly driven to extinction, likely due to their expertise in temporal mechanics. Though the race appears to have been all but destroyed, a lone Krenim colony - ironically, the colony on Kyana Prime - was able to use Annorax's research to hide their entire planet from the Vaadwaur and their Iconian masters. The player character and Captain Nog discover the colony and convince them that the Delta Alliance (the Federation, the Klingon Empire, the Romulan Republic, and several Delta Quadrant species) mean them no harm. The Krenim band together with the Delta Alliance to construct their own version of Annorax's temporal weapon ship to combat the Iconians. A rogue band of Krenim, led by the scientist Noye, become major antagonists of the Agents of Yesterday storyline as they form the "Temporal Liberation Front", consisting of the Sphere-Builders, the Vorgons, and the Na'kuhl, in opposition to the Temporal Accord.
In the novel A Pocket Full of Lies, following the events of the Year of Hell, the Krenim of the new timeline have established a variation of the Department of Temporal Investigations known as the Krenim Temporal Defense Agency. In contrast to the DTI's goal to preserve the current timeline, the Agency's goal appeared to be to use time travel to subtly ensure Krenim supremacy in the present timeline, to the extent that they altered a timeline where their past enemies, the Rilnar and the Zahl, lived on a peaceful near-utopian planet, in favor of a timeline where the two were engaged in a protracted and pointless conflict on the same planet, because the peaceful timeline restricted Krenim expansion. Having discovered 'log buoys' created by Voyager during the original timeline that were protected from changes to history by Borg phase technology, the Krenim attempted to eliminate Voyager to prevent the crew affecting their history. This attack resulted in Voyager being briefly fractured across multiple time periods in its history ("Shattered"), but when the crew were able to undo that attack, the Krenim were able to abduct a version of Janeway from the ship's history at a point before she had even arrived in the Delta Quadrant. Believing that they had eliminated Janeway as a threat to their history, the Krenim manipulated her into becoming a leader of the Rilnar against the Zahl during the aforementioned planetary conflict. Having learned about the Krenim manipulation, Voyager managed to rescue the alternate Janeway, who was taken into an alternate past to raise her daughter – conceived with a Krenim who posed as a Rilnar to manipulate her – as part of an attempt by Q to make up for some of the hardships the "Prime" Janeway had endured.
According to the All Our Yesterdays sourcebook, the Krenim homeworld is called Krenna.