The Sontaran invasion of Earth was the attempted takeover of Earth by the Sontarans for the purposes of breeding more clone warriors. (DW: The Sontaran Stratagem / The Poison Sky)
History
Background
During the early 21st century, the Sontaran Empire was losing its war with the Rutan Host. They were losing many soldiers and needed to produce more. They decided that a large planet such as Earth would be a good target, and set about their plans to eradicate Humanity and convert Earth into a cloning factory. (DW: The Poison Sky)
Beginnings
Part of their plan required the use of Luke Rattigan to market ATMOS devices across Earth, which would then be activated at the appropriate time. And so, this is what they did shortly after the Unified Intelligence Taskforce's storming of the ATMOS factory. When the ATMOS devices were activated, they pumped a thick gas into the atmosphere which had two uses - to poison Humans and to aid the growth of Sontaran clones. (DW: The Sontaran Stratagem)
At this point, many Humans died - first of all in Tokyo, Japan. As other urban areas filled with smog, many refugees escaped to more rural areas or even into the oceans. (DW: The Poison Sky)
Battle
After this point, UNIT prepared many plans against the Sontarans, including firing nuclear weapons at the Sontaran Flagship. However, this attempt was thwarted by a clone of Martha Jones, who was given a device to wipe the nuclear launch codes anf the order to repeatedly do so. This was not because it would damage the Sontaran ships - it wouldn't - but because it would ignite the clonefeed in the atmosphere and end the invasion.
Around this time, a Sontaran attack squad retook the ATMOS factory from UNIT and killed all of the Humans in the area. A short time later, UNIT prepared its soldiers from one of its nearby bases and used the Valiant to clear the smog in the area and shoot the factory, killing several Sontarans. Entering the factory once again, the Human soldiers soon decimated the Sontaran attack squad. (DW: The Poison Sky)
Sontaran Defeat
With the help of Luke Rattigan's atmospheric converter, the Doctor ignited the smog and flames spread across the Earth. When the flames died down, the planet's atmosphere was returned to its previous state. The Sontarans prepared to attack the Earth with its Fleet, however Luke sacrificed himself by using the atmospheric converter on the Flagship, causing to to explode and its fragments to destroy the rest of the Fleet. (DW: The Poison Sky) One Sontaran Pod however, piloted by Commander Kaagh, survived the Fleet's destruction and crashed landed on Earth. (SJA: The Last Sontaran)
Aftermath
After the invasion, many Humans were afraid to travel by car (as it was cars that the ATMOS devices were connected to). Other than that, life on Earth apparently continued as normal. (DW: The Poison Sky) Meanwhile UNIT took advantage of the Teleport Pods left behind in the ATMOS factory and the Rattigan Academy. This led to the creation of Project Indigo which would prove useful during the War in the Medusa Cascade. (DW: The Stolen Earth)
Commander Kaagh, the lone survivor of the Tenth Sontaran Battle Fleet, crash-landed near Goblin's Copse. Though severely injured, Kaagh repaired his ship in secret in the woods near the Tycho Project radio-telescope. His drones looked like lights in the sky, attracting human attention. Kaagh used the drones to lure Professor Nicholas Skinner and his daughter out of the radio-telescope. He kidnapped them and fitted them with neural implants to control their actions. He put Professor Skinner to work to cause all of Earth's satellites to crash land onto nuclear stations, which would cause a chain reaction and destroy the Earth, avenging the loss of his comrades-in-arms. His plans were foiled by Sarah Jane Smith, her son and his friends. Kaagh was sent home to Sontar in shame. (SJA: The Last Sontaran)