Valinor was established on the western continent Aman when Melkor, later Morgoth, destroyed their original home on the island Almaren. To defend this land from attack, they raised the Pelóri Mountains. They also established Valimar, the Two Trees, and their abiding places.
Later, the Valar heard of the awakening of the Elves in Middle-earth, where Melkor was unopposed. They proposed to bring the Elves to the safety of Valinor. However, to get Elves to Valinor, they needed to get Melkor out of the way. A war was fought, and Melkor's stronghold Utumno was completely destroyed. Then many Elves came to Valinor, and established their cities, beginning Valinor's age of glory.
There was a problem, however. Melkor had come back to Valinor as a prisoner, and after three Ages, was released on the mistaken theory that the evil had been forced out of him. After being released, he started planting seeds of dissent in the minds of the elves in Valinor, saying that the Valar had brought them here so that they would control them and claim their lands in Middle-earth as their own and that they were prisoners of the Valar. He also secretly told each of the different Elven kinds that they were superior to the other kinds and, believing his lies, the elves eventually openly spoke out against each other.
The Valar learned of this and saw what Melkor had done, but it was too late to stop him. Melkor himself, knowing that he was discovered, had gone to the home of the Noldorin Elves' High King Finwë and stolen the Noldorin Elves' prized jewels, the Silmarils, while killing the king in the process. As the Valar sat thinking of what measures to take to hinder the elves from fighting amongst each other and how to stop Melkor, Melkor destroyed the Two Trees of Valinor with the help of Ungoliant (bringing an endless night to Valinor), and fled back to Middle-earth, to his other stronghold, Angband.
The Two Trees, from which all light both in Valinor and in Middle-earth came, were dead. The last flowers of the Trees were given to two Maiar each in their own ship to sail around the world forever at different times of the day so that neither Valinor nor Middle-earth would forever be in darkness. One was called the Sun, and it shone a bright yellow. The other was called the Moon and it shone with a pale white light.
As a result of the killing of King Finwë, the majority of the Noldor, led by Fëanor son of Finwë, the maker of the Silmarils, declared their rebellion and decided to pursue Melkor, ever after known as Morgoth, to Middle-earth to win back their jewels and avenge their king. The Noldor would not listen to Manwë, the king of the Valar, telling them that they had themselves come to Valinor of their own free will and that the Valar had no desire to rule or control any of them. But Manwë's messenger said also that if they choose to leave and to fight Melkor on their own, the Valar would not help them and that they would suffer great pain and grief on their journey.
Valinor took no part in the struggle between the Noldor and Morgoth, but when the Noldor were in total defeat, the mariner Eärendil convinced the Valar to make a last blow to Morgoth. A mighty host of Maiar, Vanyar and the remaining Noldor in Valinor destroyed Morgoth's gigantic army, destroyed Angband completely and threw Morgoth into the Void.
During the Second Age, Valinor made a single action: the building of the island Andor as a reward to the Edain (who had fought with the Noldor), where they established Númenor. Soon the kingdom of Númenor grew powerful, and even tried to invade Valinor. Then Eru Ilúvatar was called upon by the Valar and the island was destroyed, and Aman was lifted into the sky as the rest of the world was made round.
During the Third Age, recognizing that an outright confrontation with Sauron (Melkor's beloved Maia) would be disastrous, the Valar sent the Istari to Middle-earth with the intent of giving counsel to Men in their resistance to the growing power of the Dark Lord.
Many Sues state that they come from Valinor or have Valinorean ancestry. Occasionally they may even be the non-canon children of two Valar (mostly Manwë and Varda). While the Valar having progeny was part of past canon (see the Lost Tales books), that is not the case today. Swords of Sueness can also come from Valinor, with Aulë or the Fëanorians supposedly forging them.