(covers information from several alternate timelines)
The Krenim Imperium was the sovereign state of the Krenim people, located in Grid 005 of the Delta Quadrant, over 60,000 light-years from Earth. The Krenim rose to power based on their mastery of temporal science, which allowed them to create fearsome weapons such as chroniton torpedoes that could penetrate deflector shields. At its height, the Imperium spanned 5,000 parsecs and controlled thousands of warp-capable vessels, over 200 star systems, and some 900 planets.
In the 2170s, the Imperium had declined greatly due to conflict with the Rilnar. Annorax, a Krenim military commander and temporal scientist, sought to reverse this state of affairs by building a weapon ship that could erase targets from the space-time continuum. With it, Annorax destroyed the Rilnar and restored his people to glory. However, the elimination of the Rilnar indirectly led to a plague that devastated the Krenim, necessitating another temporal incursion. Over the next two centuries, Annorax erased countless civilizations from history, but could never achieve the full restoration of the Imperium that he desired. (VOY: "Year of Hell", "Year of Hell, Part II")
In one possible timeline, the USS Voyager encountered the Krenim on stardate 50973. Over the following year (dubbed the "Year of Hell" by the Voyager crew), Voyager suffered severe damage and heavy casualties battling Krenim warships as it traversed the Imperium. (VOY: "Before and After")
In another possible timeline, the USS Voyager encountered the Krenim in mid-2374. The region was then dominated by the Zahl, whose elimination by Annorax resulted in a 98% restoration. Again, the Voyager crew endured a "Year of Hell", battling the warships of the restored Imperium. However, in this timeline they managed to develop temporal shielding to defend against chroniton torpedoes. Unexpectedly, the shielding also interfered with Annorax's temporal calculations, leading him to inadvertently reduce the Imperium to a pre-warp state with the erasure of the Garenor. Annorax attempted to erase Voyager to correct this mistake, but failed to do so.
Ultimately, the Voyager crew forged an alliance with the Mawasi and the Nihydron and attacked the weapon ship. Captain Kathryn Janeway set Voyager to collide with the weapon ship, triggering a temporal incursion that erased the ship from history. The original timeline, in which the Imperium was a medium power in contest with its neighbors, was restored. In this timeline, Voyager peacefully circumvented Krenim space on the advice of a Krenim commander. (VOY: "Year of Hell", "Year of Hell, Part II")
The novel A Pocket Full of Lies features the Krenim as antagonists manipulating the timeline in order to ensure Krenim supremacy.