Due to "The Young Descendant of Tepes", the title of the prelude theme to the final boss stage of Embodiment of Scarlet Devil, she has been sometimes linked to Count Dracula's lineage. This is because Dracula's full name is Vlad Ţepeş Dracul. However, ZUN denied that she is related to the Dracul family, although in character, Remilia herself asserts that she is a descendant of Ţepeş. Some fandom state that she is lying however.
Like most vampires, Remilia has the power of shapeshifting at her disposal and can change into a bat. However, unlike most vampires, her wings remain visible even when she is in human form, making it impossible to pass herself off completely as a human.
In Perfect Memento in Strict Sense, Remilia stated that when she arrived in Gensokyo, she killed all the other vampires that habited there, but later, it was revealed that Remilia lied to Hidea no Akyu in some facts. So this maybe a lie.
Remilia is not only Sakuya's master but the one who gave Sakuya her name (according to Perfect Memento). Considering Sakuya's murky past and the unlikelihood of a human becoming a vampire's servant, the leading theory is that Sakuya was once a vampire hunter, and Remilia earned Sakuya's servitude by besting her in combat.
According to Gensokyo's timeline, Remilia was born in the year 1502, making her, as well as her sister and Toyosatomimi no Miko, three of very few characters whose birth dates are actually known.
One of Remilia's weapons is the Gungnir, a spear that is described as having the ability to always hit its mark. You could say, the target is fated to be hit, making it a very fitting weapon for Remilia. Like Flandre's signature weapon, Remilia's Gungnir holds a strong magic, but at a lesser level than Flandre's Lævateinn.
It is quite coincidental that Remilia's appearance was in the 6th Touhou game. She is the Stage 6 boss, and the player will fight through 6 spell cards on that stage on any playable difficulty (Remilia has 5 spell cards total and Sakuya has 1 on that stage). When these numbers are all put together, it reads "666", best known as the "Number Of The Beast".
Much like her sister when using a bomb on her last spell card, she turns into a bat to avoid them.
Some fan works have postulated that Remilia uses her power to manipulate fate unconsciously. Otherwise, it would be far too great a power. For instance, if she was able to control a person's fate actively, she could have made it Reimu's fate to lose to her. However, ZUN has hinted otherwise in Sakuya's Perfect Memento in Strict Sense article, where Akyu has speculated that Remilia may have manipulated Sakuya's fate in such a way that she could have a more friendly relationship with other human beings. Should that prove to be true, it would mean that Remilia can indeed intentionally, or at least consciously, manipulate fate.
In Unthinkable Natural Law, if the player places a custom parasol system card in Remilia's deck, she'll be able to fight in stages outside.