Diana invites Kogorou and Ran to London, but since Conan cannot travel with his invented name, Ai gives him a temporary antidote, letting him travel as Kudou Shin'ichi. Together with Professor Agasa they are on a plane to London. Back in Japan, Ai now lives with Ayumi. Near their apartment, a suspicious man clothed in black named Kurokawa Youji has been trying to track down and now has found Ai. Shortly after Mitsuhiko notices a picture in a magazine of a foreign actress named Grace Aihara, who looks exactly like Ai, Conan calls, ominously instructing Mitsuhiko to keep Ai away from the Professor's house. And so, Mitsuhiko and Genta go about trying to protect Ai... (Source: foo2)

In this entirely new story produced specifically for the DVD, Conan leads a group of young detectives against the phantom thief Kaitou Kid, who has his eyes set on a jewel at a hotel on an isolated island. (Source: ANN)

This OVA takes place ten years in the future and chronicles the possible events if Conan Edogawa and Ai Haibara do not take the antidote to APTX 4869 and grow up alongside their friends Genta, Mitsuhiko, and Ayumi, while still maintaining their detective endeavors.

Sonoko is writing a script for a play. In her script, there's a murder case, and high-school detective Suzuki Sonoko is there to help solve it. Haibara finds flaws in the deduction section of the plot, and Ran decides to call Shinichi for help with the script. (Source: Wikipedia, edited)