They appear to be a type of mechanical based lifeform. (DS9 video game: The Fallen) Its been noted that no Grigari construct has been able to overcome a life or death situation without attempting to bargain for its life. (DS9 novel: The War of the Prophets)
The Grigari made extensive use of nanotechnology which was the secret of their medical technology. Through the use of molecular assembly devices, they were capable of expertly weaving together steel and flesh; uniting the nervous system of a living organic being to link directly with the computer control circuits. Once done, the process did not end as the flesh of most lifeforms often rejected the filaments of connection that the Grigari devices wore into the body. As such, the devices were programmed never to stop and in order to continue to maintain the connection. This meant that each layer of living cells became damaged by the nanotechnology which stripped away the organic tissue and replaced it with more filaments. The living body in the end became a Grigari amalgam which was completely discarded with an inexact mechanical subtitute. (TOS novel: Federation (novel))
Their culture is based on piracy and, unlike the Ferengi, they will resort to unsavory tactics to make profit. (DS9 video game: The Fallen) The Grigari themselves often claimed themselves as being traders that had come to offer the secrets of eternal life to unsuspecting worlds. When their treatments were later investigated and found to be hideously flawed, the Grigari typically left as one where they moved to other uncharted sectors of space leaving behind the gruesome tales of the horrors their painful technology had wrought on those planets that had dealings with them. (TOS novel: Federation (novel))
In 2267, the USS Enterprise encountered a Grigari vessel, allied with former WWIII leader Adrik Thorsen. They demanded of Kirk and bridge crew full cooperation for the whereabouts and apprehension of both Zefram Cochrane and wife Nancy Hedford/Companion. Mr. Spock also noted that the Grigari commander has cybernetic growths that extended into the microscopic level for better access to systems. (ST novel: Federation)
In 2374, a group of Grigari were hired by Obanak Keelen to obtain the Orbs of the Pah-wraith. These mercenaries would have numerous encounters with the crew of Deep Space 9. This group of Grigari would be killed on Deep Space 9, either by the Starfleet crew or under the influence of the Pah-wraith possessed Obanak. (DS9 video game: The Fallen)
The Grigari feature heavily in the alternate timeline generated by the start of the War of the Prophets. They were encountered when the Red Wormhole was formed and a Dominion fleet was sent into the anomaly to determine whether it connected to the Gamma Quadrant. However, it was learnt that the wormhole actually connected to the Delta Quadrant. All the crew of the ships were believed to have been killed with Weyoun being the only survivor. He returned to the Alpha Quadrant, changed by the Pah-wraiths, with the Grigari who served as the military arm of the newly formed Bajoran Ascendancy.
The Grigari forces attacked the Dominion and Cardassian force to bring an end to the Dominion War. The offer of surrender was given but was refused. As a result of this, the Grigari wiped out all the worlds of both races leaving nothing standing. In 2375, the Grigari freed Thomas Riker from his imprisonment on Lazon II. The former Starfleet and Maquis member decided to join the Grigari forces.
Several Grigari forces were invited to Sector 001 in 2388 to take part in trade negotiations. However, the Grigari were confused by a transmission and opened fire. The Enterprise-F was destroyed by the Grigari in the process. They would be responsible for the destruction of Earth, spread a Nanospore plague to the majority of Humanity almost wiping out the species and destroy a large Klingon armada, which resulted with the destruction of the Klingon Empire by use of transporting weapons from the mirror universe into the known universe which tore apart worlds and rendered atmospheres unbreathable. They were later present on the planet where the Guardian of Forever was located to stop Starfleet's attempt at using the ancient machine to travel back in time to defeat the Ascendancy, as the battle closed the Grigari detonated a singularity bomb that wiped out everything on and around the planet. (DS9: novel series: Millennium)