Ever since the Fire Red and Leaf Green pokemon games introduced the union room and some wireless capabilties, visa vis the wireles adaptor, the pokemon games have continued to introduce new wireless features, most recently through the GTS and other internet capabiltiies with diamond and pearl. This article provides a breakdown of the various wireless functions we've had throughout the pokemon games.
The union room has continued into the fourth generation as a stock local function, essentially replacing the link cable that was used for ruby and sapphire and the previous generations. In FRLG when it was first introduced, and it generally continues to be used in this fashion, the union room exists in every pokemon center and when you enter the union room you can see anyone else who is in the union room (using a wireless adaptor obviously) within about 25 feet, generally speaking. It's somewhere between 20 and 30 feet, iirc.
Within the union room you can start a 'limited' conversation with a trainer or challenge them to a battle. Trading offers are put up on the wall in the upper left corner of the room.
Pokemon Emerald also went wireless with the trading information capability, which is especially useful to assemble secret bases in your game.
Diamond and Pearl of course have introduced the GTS (Global Trade Station), friend code capabilities, and other fun stuff.
Diamond and Pearl of course allow you to register friend codes using the Pal Pad which also allows you to check your friend code roster and check what your own friend code is. Connecting to the nintendo wifi connection will allow you to battle or trade with any of those people who's friend codes you have registered in your pal pad, and who are also connected to the nintendo wifi conection. Voice chat is also automatically enabled for battle, though it's effectiveness is rather questionable.
The Global Trade Station (click to go to the official site) functions as an integral part of the diamond and pearl wireless functions. Essentially, if you've not used it already, the GTS allows you to put one of your pokemon up for trade and then specify what you're looking for in return. The system automatically handles the trades and if and when somebody decides they want your pokemon, the system will automatically trade the two, and the next time you hop onto the GTS, your new pokemon will be downloaded into your game. On the other side, you have the option of searching through the GTS to find a pokemon that you want to trade for. According to the GTS official site, as of December 13th, 2008, there were 1,986,029 across the world, people using the GTS to trade for pokemon. The actual in game building for the GTS is located in Jubilife City. But, fear not if you hate adding friend codes or for some reason don't know many people with the game. The Battle Tower has you covered with a facility for pairing you off with people through the nintendo wifi connection, no friend code required.
The Mystery Gift function has also returned, from GSC, for Diamond and Pearl. According to serebii, you need to tell a man on the second floor of jubilife city, "EVERYONE HAPPY" & "WI-FI CONNECTION". Can't remember myself if that's true or not, been a while since I've been at that part of the game. Regardless, you can mystery gift with your friends but the mystery gift function is now a days used for nintendo events where they hand out pokemon; so you'd select "get via wireless." Also, via nintendo wifi connection is how Nintendo is now handing out event stuff as well, and all it takes is a router or other internet connection to hook up to your ds/lite and you'll be able to download stuff, such as the secret key event.
The Underground also has some wireless facilities in Diamond and Pearl, but they just use the ds wireless abilities, same thing that you'd use if you were in pictochat with your friends. Accessing the underground is really pretty similar, just need to get the appropriate kit in Eterna City. The underground is not connected entirely however, and where you appear underground is, obviously, relevant to where in Sinnoh you entered the underground. So to get to some areas of the underground you'll need to move to a different area of sinnoh. You can find a whole bunch of different items in the underground and also can create a secret base and go underground with a friend, play this flag mini game, visit each other's secret bases, etc.
As if Platinum wasn't changing the way we look at pokemon enough, it also brings several new wifi innovations, such as the Wifi Square, found in pokemon centers. It's essentially a group wireless function, such as some of the wireless minigames in FRLG. The WiFi Square's appearance can change based upon type; water, fire, grass, etc. The Wifi Square though does have a maximum time limit, presumably to serve as a spam deterrent. Platinum also provides us with a new wifi club with different activities, such as a poffin making game. It also provides you with a union room esque function, but it's connected to the nintendo wifi connection, i believe, which obviously makes it much more interesting then the previous limitations on the union room.