Every Final Fantasy game has its spin on how Chocobos are utilized to travel around on the map. Final Fantasy VII, however, has one of the most innovative Chocobo systems in the series. First off, you can only meet Chocobos if you have the "Chocobo Lure" materia equipped. This will allow you to meet Chocobos in battle alongside other monsters when you travel across Chocobo tracks on the map. In order to catch a Chocobo, you have to defeat all the monsters before it runs away. This will allow you to use a Chocobo for a while. Be careful, though, as until you buy stables in the Chocobo Farm (which can only be done after Meteor is summoned), Chocobos will always run away after you catch them. Secondly, there's the racing system. After you have your own Chocobo(s) in the stables at the Chocobo Farm, you can enter races in the Gold Saucer. The more you win, the tougher the races become. You can also get different colours of chocobo, for example a Golden Chocobo can cross water and mountains.
The two staples of any Final Fantasy game when it comes to transportation on the overworld map are Chocobos and Airships. Well, guess which one the Highwind is. That's right, it's the Airship. Acquired in Disc 2, the Highwind allows you to fly anywhere on the map with one slight drawback: it can only land on grassy plains.
Allows you to travel under-water. You have to use the submarine to get to fight with Emerald Weapon.