The Moon Kingdom was located at the Sea of Serenity on the Moon. Silver Millennium was inhabited by beings with very long lifespans, whose mission was to help Earth people progress. The princess of the Moon, Princess Serenity, was in love with Prince Endymion of the Earth. However, the people of Earth were corrupted by Queen Metalia and encouraged to hate and fear the people of the Moon.
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Anime
In the anime, Queen Beryl led the invasion and destruction of the Moon Kingdom, killing all who were in the way, including Princess Serenity and Prince Endymion. Queen Serenity used the Silver Crystal to defeat the enemies, but using so much power weakened her greatly. Seeing that her kingdom was destroyed and her daughter killed, she used the last of her power to send the prince, the princess, her guardians, and her advisors, the cats Luna and Artemis, to the future on Earth.
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In the manga, the story was mostly the same with some slight differences.
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Instead of Queen Beryl killing both the Prince and the Princess, she only killed the Prince as he was protecting the Princess. In her sorrow, Princess Serenity took her own life with his sword.
After Queen Serenity sent everyone to the future in the manga, the three talismans of Sailor Uranus, Sailor Neptune, and Sailor Pluto activated to awaken the soldier of silence, Sailor Saturn. Sailor Saturn dropped the Silence Glaive and Silver Millennium was turned to dust. The remaining Sailor Senshi were also destroyed.
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In the present, during the final battle with Queen Metalia in Act 13, the Moon Kingdom was restored (albeit empty) by Sailor Moon's power.
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Almost nothing was revealed about the Silver Millennium in the live-action series. In flashbacks, the Moon Kingdom was shown encased in a crystalline dome, and appeared to be simliar to the manga version. The inside of the palace was shown during Sailor Moon's transformation into Princess Sailor Moon, and it had a crystalline structure much like that of Crystal Tokyo.
The moon itself had a barren, cratered appearance, with only the encased kingdom seeming to be habitable.