The Remote Play function on PlayStation 4, which is currently available for PlayStation Vita, is on it's way to both PC and Mac. This has been confirmed by Sony President Shuhei Yoshida on Twitter.
These news were announced shortly after the announcement of an unofficial app about to release, which will let you play your PlayStation 4 games via your PC. The unofficial app will cost you $10 while Sony's app will likely be free.
Whether Sony was already working a Remote Play function remains unknown, but the timing of the announcement sure indicates that Sony would prefer their players to stick with the official app.
Playstation 2 emulation
More opportunities for Remote Play is only one of several things that Sony is currently dabbling with. The Japanese company announced last week that they are working on making sure that PlayStation 2 games can be played on PlayStation 4.
We are working on utilizing PS2 emulation technology to bring PS2 games forward to the current generation. We have nothing further to comment at this point in time.
The above statement indicates that the PlayStation 4 console indeed will be able to play PlayStation 2 games, but there is nothing to indicate that this technology will also enable physical games to be played. In other words you should not dust off your old PlayStation 2 collection quite yet.