The Unicorn Chronicles

The Unicorn Chronicles is a young adult series by fantasy writer Bruce Coville, chronicling the journey of a young girl named Cara through Luster, a land populated primarily by unicorns. Pursued by mysterious forces, she is forced to leave behind her life as an Ordinary High School Student and is sent to Luster by her grandmother with a mission to deliver a message to the Old One. Along the way, she uncovers the history of Luster and the unicorns, as well as some amazing things about her own family.

As of the present, the books are

Into The Land of The Unicorns (1994)
The Song of The Wanderer (1999)
Dark Whispers (2008)
The Last Hunt (2010)

Also, Coville's anthology A Glory Of Unicorns includes a short story about the Guardian of Memory, told from Ivy Morris' point of view.

Tropes used in The Unicorn Chronicles include:

The Aloner: The Guardian of Memory
Exclusively Evil: The unicorns treat the delvers this way. The delvers think of themselves somewhat differently, though.
Bigger on the Inside: Thomas' cart.
The Big Guy: The Dimblethum in the first book. He shares the position with Finder in the second.
Chekhov's Gun: Cara's missing last name, and the song that Medafil's shell sings
Chronic Hero Syndrome: Unicorns are drawn to distressed maidens by instinct ( this is how Moonheart first meets "Ivy Morris", by the way). Knowing this, Hunters often use young girls as bait to lure out unicorns.
Dating Catwoman: And at least initially, it worked out. Cara's maternal grandmother was a unicorn permanently transformed into a human, and the connection to unicorns seems to have passed itself down to the succeeding two generations. Cara's father was a descendant of, and follower of, Beloved, and a hunter of unicorns. It seems the parents never learned each other's secrets, but the mother is long gone when the story starts. However, she returns by the end of the series.
Evil Old Folks: Beloved.
Face Heel Turn: The Dimblethum
Fantastic Racism
Fate Worse Than Death: A unicorn heals wounds by piercing the injury with its horn, leaving a star-shaped scar. The process is incredibly painful, but only for a moment. So what would happen if the horn broke off in the injury and could not be removed? Beloved is immortal with the horn in her heart, but the pain never leaves her.
First-Name Basis: Cara through most of the first book. It turns out her last name's Hunter.
Foreshadowing: In the very first book, the Dimblethum's introduction describes him as resembling nothing so much as "a man that started to turn into a bear, but stopped before the process was complete." In the final book, it's revealed that that's almost exactly the case.
Grumpy Old Man: Arguably Moonheart. He's got the personality, but it's not clear whether he qualifies as "old" by unicorn standards. Younger unicorn Lightfoot certainly thinks of him this way. Grimwold the dwarf is a more obvious example of this trope.
Half-Human Hybrid: Due to the true nature of her grandmother, Cara is part unicorn (it's complicated). Also, the Dimblethum has the appearance of being half-human and half-bear, but it's unknown why he's that way.
Heart Trauma: In order to communicate with unicorns, your heart must be pierced by a unicorn's horn.
Heel Face Turn: Cara's father
Here There Were Dragons: Creatures such as unicorns and dragons used to live on earth, but human persecution forced them to migrate to other worlds (Luster, in the case of the unicorns).
I Am Who?: The Dimblethum is Elihu, Luster's creator.
Interspecies Romance: Arguably Jacques and Ivy Morris
Last of His Kind: Implied to be the case for the Dimblethum and the Squijim. The dragons arguably qualify, there's only seven left.
Living Relic: The Guardian of Memory, whose job is basically to be the only unicorn on Earth.
Love Confession: Finder to Belle as he's dying
Luke, I Might Be Your Father: It's suggested that Jacques is Cara's grandfather, but for the characters there's no way to tell for sure.
Luke, I Am Your Father: It turns out that Ivy Morris is the granddaughter of Arabella Skydancer. Also, Cara is the daughter of one of the Hunters and descended from Beloved.
Magic Land: Luster
Never Mess with Granny: Beloved is extremely old, but she can kick ass.
Nice Job Breaking It, Hero: The basis for Beloved's vendetta against the unicorns is a misunderstanding between her father and a unicorn who tried to help her.
One Degree of Separation: Cara's family tree is very... extensive.
Opposites Attract: Belle (small but rough and aggressive) was a Love Interest for Finder (mellow Big Guy).
Our Gryphons Are Different: Medafil is pretty much a classic gryphon. He even hoards treasure.
Redheaded Heroine
Revenge: Key motive for Beloved.
Schedule Slip: Fiveish years between the first book and the second, and another nine years between the second and the third. The fourth came out two years from the third's publication. If you were a child when the first book came out, you've probably graduated from college by now.
The Squadette: Belle, who is part of the Queen's Guard.
Soul Jar: Cara briefly carries a dragon's soul jar in the first book, and astonishes the dragon by immediately returning it. In gratitude, the dragon grants her the gift of languages.
Take Our Word for It: In the first book (two pages from the end) Cara and her companions make the final trip to Summerhaven. We're told that the journey there was "filled with marvels and wonders" and get no elaboration on any of it.
Team Pet: the Squijim
Theme Naming: The centaurs have Greek names.
True Neutral: Luster's dragons. Until The Last Hunt, anyway.
Walking the Earth: Most of the humans in Luster are nomadic.
Wandering Minstrel: The Queen's Players
What Happened to the Mouse?: in Song of the Wanderer, We hear the story of one of Luster's dragons, who has been trying to get to the world created for dragons, where his lover went. His story is never resolved.