I'm assuming/hoping you're talking about Remote Play with PSVita?
Because there's a wall of text incoming, and it would be a shame if I wrote all of that for nothing :I
I have occasionally connected my Vita to a friend's PS4 (and even PS3, once).
First, I'll get the PS3 out of the way:
It comes across as an afterthought (which it is). The button's, I feel, are not very reasonably mapped (to input R2, press SELECT+R. Or something along those lines. Wat.)
It worked, in that I could control the PS3 home menu, but if you want to play games, they have to actively support the Remote Play feature. And apparently, very few titles actually do.
PS4, on the other hand:
Everything works much better. Pretty much every PS4 game out there is compatible with Remote Play (just check the back of the game box). The button layout can vary between games, though. That is to say, whatever buttons the Vita shares with the PS4, are mostly identical. But since the Dualshock4 has more buttons overall, the designers have to get creative with the Vita's front and rear touch pad, to emulate the missing buttons. Some configurations work well, some not so much. It depends on the game.
Dark Souls 2 SotfS had everything on the front touchscreen: the center of the screen was the Ds4 touch pad, the upper left and right corners were L2/R2 respectively, and the lower corners were L3/R3. But if you know your controller [and you should

], you might realize the problem here: Everything is pressed via thumb now, except for L1/R1. Meaning that for a few inputs, the thumbs are on their own. It's especially bad when you need to press L3/R3, because you have to take your thumbs off the Control Sticks. But for Dark Souls, this layout is barely a problem.
Supersonic Acrobatic Rocket Powered Battle Cars 2: Electric Boogaloo
Rocket League switches L1/R1 with L2/R2, which is a very good thing. Accelerating with the rear touch pad wouldn't feel right, and doing it with the touchscreen would be nearly impossible.
Metal Gear Solid: Ground Zeroes mapped L2/R2 and L3/R3 to the rear touch pad instead (it might also have switched L2/R2 and L3/R3 upside down, but it's been a while). I believe that makes sense, but you better know damn well where the rear touch pad begins and ends. I always had to try multiple times to hit the corners correctly.
I have not tried Remote play via different Acess Points yet, but I can tell you that it needs a reasonably fast and stable internet connection. There's an option to reduce the quality of the video feed, if your connection ain't that great; but even then, you propably won't be able to Remotely Play via mobile internet (if that was your plan).
Overall, Remote play is a pretty sweet feature. It doesn't work as well as the Wii U's Off-TV Play, but then, how could it. But if I owned a PS4, you can bet I'd use it quite often, because gaming in bed or on the toilet is awesome.
Oh, and you can not connect 2 or more Vitas simultaneously.
Hope this is at least somewhat useful!