Frieza and Cold's invasion on Earth is a conflict which occurred differently in two timelines: the main one depicted with Future Trunks interrupting the normal course of events, and another one where no time traveler comes, and Goku saves Earth.
Sometime after Frieza's defeat on Planet Namek by Super Saiyan Goku, his father and true boss of the Frieza Force, King Cold, and his direct henchmen are informed of the younger tyrant's defeat and go out looking for him in the area of Namek's ruins, only to find the dying dictator's shattered remains floating in space unconscious.
After being taken by Cold's men to King Cold's planet and getting recovered in the Medical Machine, Frieza's body is attached to synthetic modifications made by a team of surgeons led by Malaka and is now even stronger and faster than ever before. Frieza asks his father to change their course of movement to Earth so he will be able to avenge the Saiyan who did this to him. Cold agrees and commands his henchmen to set King Cold's spaceship to the destination Frieza ordered.
Upon Frieza's near arriving to Earth, Gohan who is waiting for his father to return from Planet Yardrat (where he's training) for the past year, and has a nightmare about his father isn't really coming back while Frieza is coming to attack him, once he wakes up he senses Frieza's evil Ki approaching towards Earth, both Krillin and Master Roshi sense it too, in the Capsule Corp. Vegeta and Yamcha sense Frieza's power level too, amazed at how could he survived the Battle on Planet Namek. Tien and Chiaotzu who are training in the snowy mountains sense the two huge kis too. Krillin contact Gohan via phone and asks him if he knows what to do, Gohan replies that he does. The young Saiyan hybrid quickly changes his outfit to the Battle armor he wore on Namek and flew out his window, leaving his mother, Chi Chi, and grandfather, Ox-King, behind. The entire Dragon Team rush over to where Frieza and Cold are supposed to touch down in the Northern Wastelands.
In space, Goku, who sensed Mecha Frieza's improved power coming to Earth is rushing towards his Earth, only that his Ginyu Force space pod is slower than King Cold's spaceship and he's running late when the two tyrants are about to arrive on Earth. It turns out Bulma and Puar followed Yamcha and Vegeta's tracks with Bulma's airplane and are also present at the battlefield much to Yamcha's surprise, he tries to tell them to go back home as it is far too dangerous for them, but Bulma is stubborn and says she came to see how Frieza really looks like since she missed seeing him on Namek despite knowing he will probably blow up the planet while getting there.
The Z Fighters who estimate Frieza's power level understand he's suppressing his true power like he did on Namek, but even if he won't be fighting seriously they (excluding Goku) have no chance of defeating him. They also mentioned that Frieza has brought "another one like him" referring to his father, like one of their kind alone wasn't enough. The amazed Z Fighters mask their power levels and try to figure out a plan to win the battle. Vegeta who does not believe the Earthlings can win against Frieza commands everyone to not use their energy so they won't be picked up on the tyrant's scouters. They decide to walk the not so long way to Frieza and Cold's whereabouts while the tyrants themselves are already out of the ship and are examining the planet. Frieza then commands 3 of his soldiers to take off and kill every human they're coming across. At this point the time line splits into two different ones:
- In the original Future Trunks' timeline Goku, who is still on his way to Earth, uses the Instant Transmission technique to teleport himself to Earth while his ship still has 3 more hours to go, and easily defeats both Mecha Frieza and King Cold.
- In the timeline presented in both the manga and anime, just as Goku is about to launch himself to the battlefield, another unfamiliar strong ki appears out of nowhere thus stopping Goku from proceeding with his technique, it was Future Trunks who just recently traveled back in time to alert the Z Fighters about their awful demise in the future by the Red Ribbon Androids who were created by Dr. Gero. The youth does not know the entire details of the fight against Frieza on Earth and is unaware of Goku's new technique thus believe he will not be home at least 3 more hours. Future Trunks steps in to Goku's role and changes time forever. After slicing the 3 henchmen mentioned earlier to pieces with his sword, the teenager mocks the two tyrants, telling them that he will kill them (much to their amusement). Frieza orders his foot-soldier, Iru, to take the sassy Earthling out. After scanning his opponent and mistaken him to be a weakling with a power level of only 5, Iru blasts the youth with his Arm Cannon which Future Trunks easily deflects before replying with an melee attack of his own, killing Iru in front of the entire standing forces of Frieza's army. Frieza then commands all of his soldiers to surround the youth and take him down, which they try to do with a rush attack, only to be sliced to death as well. In the anime there is one soldier who survives only to be killed by Frieza for showing fear (in the Japanese version it was because he stood in the tyrant's way). After he easily kills all of Frieza's Subordinates (which is sensed by the Z Fighters who are standing behind a nearby mountain), he then transforms into a Super Saiyan as well, much to Frieza's fear and disbelief due to his trauma from Goku on Namek, and challenges Frieza to fight at his maximum power, where he's proven no match against the Saiyan hybrid. Trunks uses the moment Frieza thought he killed him and brags about it to his father to launch a God Breaker attack at them, causing them to fly above the attack and then surprises Frieza from above. The shocked tyrant is then sliced in half before immediately being sliced into dozens of pieces and then burnt until there is nothing left of him, finally killing him - much to Cold's astonishment and the Z Fighters' disbelief. Cold then asks the young Super Saiyan to land down to the ground with him. He congratulates him for defeating his son and says that he is really the "strongest in the universe", he then offers Future Trunks to join his empire and to take Frieza's place as his son and heir. Future Trunks declines the offer, causing Cold to get angry at the "disgreatful" youth, planning to attack him and engage a battle with him. After coming to a false conclusion that the youth's extremely high power level is only due to his possession of his master-crafted sword, King Cold asks the youth to give him the sword so he can examine it. After Future Trunks hands over his sword, King Cold then declares that he will kill Trunks with it. Attacking Future Trunks, his strike is easily caught and blocked by Future Trunks. Future Trunks then shoots an energy blast through Cold's stomach. Cold is knocked into a close mountain's surface where he cannot move (the Z-Fighters watches the entire scene from nearby after Frieza was killed), he then asks Future Trunks to spare his life and vows that he will give him many planets and galaxies if he will do so (in the Funimation dub he says that while his son was evil, he was not like him, but wanted "global peace"). Future Trunks then decline his offer again and shoots a much larger energy wave at him, killing him and bringing the Cold family reign of terror across the universe to its end. He then destroys King Cold's spaceship with a single blast as well (in Dragon Ball Z: The Legacy of Goku II, it is said that the Capsule Corporation scientists are checking it's remains in their labs). He invites the amazed Z Fighters to come join him waiting for Goku. While Goku arrives 3 hours later and spares with Future Trunks, before being informed of the bad news about their future, Future Trunks states that considering Goku's Super Saiyan power level is stronger than his own, he could have easily killed both Mecha Frieza and King Cold.