Novarama have been plotting for some time on how to do Invizimals justic on the Vita. And they've come up with quite a clever way to trap them. Catch the little buggers in the real world on your portable, then suck them into your PS3 and play in "their" world in a more traditional adventure.
There are two games to bring this all together, Alliance on the Vita and Lost Kingdom on the PS3. Hopefully, you get the drift from this Spanish video, I'll update when the English version becomes available. With cross-play helping shuffle data around, all that we need to know is if the capture games are an improvement on the rather wobbly PSP efforts.
Update: A PSN blog post explains it all.