Shyvana's ultimate, Dragon's Descent, is the only non-toggle champion ability in the game that is not cooldown based.
Shyvana's dance is from the music video RIVER by the Japanese idol group AKB48. A side-by-side comparison of the dance can be seen here.
Shyvana's lore was changed after release, removing references to being attacked by a mob and instead having Jarvan IV save her from the wrath of the dragons. This change was done because it was felt that the original lore did not make it sensible for her to join Demacia.
Shyvana was the first champion since Kog'Maw to not receive a League Judgement. With the exception of Varus, no other champion since then has received a Judgement either.
Shyvana's rage system was mislabeled as "Dragon's Blood" on her mechanics preview.
Shyvana is the third champion to feature a physical transformation ability, the others being Nidalee and Swain released before her, and Zyra and Elise released after her.
Ironscale Shyvana is a reference to the scale armour worn by warriors of different cultures.
Scale armor is often associated with dragons in various fantasy genres. This is most likely due to how the individual metal scales are overlapped with each other, resembling the fictional scales of a dragon.
Moved by Shyvana's plight, Jarvan IV assisted her in slaying the mighty dragon that killed her father. After the battle, Jarvan IV offered Shyvana a place as a noble warrior in the ranks of the Demacian Elite Guard. Out of gratitude and necessity, Shyvana accepted.