At one point in the story of Alice's Adventures in Wonderland, Alice crawled through a rabbit hole, which went on like a tunnel until it suddenly dipped downward, causing her to fall into a very deep well. Michael Burnham quoted this part of the book in 2256, when she was crawling through a Jefferies tube on the USS Glenn.
She later told Cadet Tilly that what she had learned from the life that Alice lived was that the world did not always adhere to logic, that what was down could be up and vice versa, and that when you were lost, you could be found. (DIS: "Context Is for Kings")
In 2257, when the USS Discovery intercepted a priority one distress signal from the USS Enterprise, Michael Burnham suddenly remembers when she was a child and her foster mother was reading Alice in Wonderland to her, and there were black and white drawings of Alice on the pages of the book. (DIS: "Brother")
In 2267, while on the Shore Leave Planet, McCoy mentioned to Sulu that the idyllic planet was like "something out of "Alice in Wonderland." In response, the planet created robots representing the White Rabbit and Alice, basing them on his memories of that tale. The appearance of these two characters was the first clue that all was not as it appeared on that world. (TOS: "Shore Leave")
McCoy and Sulu briefly encountered Alice again, when the USS Enterprise revisited the Amusement Park Planet in 2269. Like before, Alice was seen chasing the White Rabbit. Later, the two officers had a picnic lunch with Alice, the White Rabbit, and a dragon. (TAS: "Once Upon a Planet")
After Kirk and crew time traveled from 2286 to the 20th century to save Earth from the Whale Probe, Kirk beamed Gillian Taylor aboard their captured Klingon vessel, and when she materialized, he said, "Hello, Alice. Welcome to Wonderland." (Star Trek IV: The Voyage Home)