So... there's probably already a post somewhere about this but I want to find out if you can still trade Pokemon across game systems like a 3DS and a DS or 3DS XL for example?

To give you all some idea of where I'm coming from the only game I got to have when I was little was a gameboy color and later an SP, mostly we played pokemon. Back then you could trade with a nifty cord.
I've been away from gaming thanks to an ex for a very long time, since they were extremely into it and did nothing else...so I got to do everything else.

Anyhow, now I have a 3DS and am starting back into things with Pokemon Pearl, one of its companion games and a handful of others. I've heard you can trade via wifi and later heard that that network was shut down about two years ago sad

What's the definitive explanation on the subject?
I think most players would like to beat a game....