Other than the slightly vague "summer" tag we've been given, the general Vita population have no idea when PlayStation support will be added to their favourite handheld. It's fairly frustrating, because it's obviously a feature that lots of people want and, personally, I've been waiting to play several PS1 games specifically on my Vita.
Sony have released a press release in Japan that reveals that firmware 1.8 is on its way, and with it comes PlayStation 1 support. Still no more specific a date than "summer," but depending on how you look at it, there's only so much left of summer and the leap from 1.69 to 1.8 isn't a huge one. That's not to say Sony definitely won't make the jump in increments, but it's obviously the main firmware they're working on at the moment.
I'd like to think that the firmware will be released when it's ready, which is why Sony have yet to pin a date on it. Still, firmware 1.8 really can't come quickly enough.