Depending from what country you call from, depends on how 'great a heritage' skylines ....
Going back to the arky days of Prince, they released the first Skyline in 1957, the ALSIS-I, which was a shocker, and it really wasn't until they released Skyline GTS54, that the standard cars started fairing quite well when compared to the local talent..
After Nissan bought out Prince, they released the S20 powered PGC10 Nissan Skyline GT-R, which was pretty awesome with 160ps, twin piston front discs, finned alloy rear drums, reverse dogled 5 speed g/box( rare in Japanese cars in 1967), lsd and a factory 7000 redline! A great car, which is darm near impossible to find on the road these days, but not nearly as well known as the successing model; the KPGC10 GTR, or HAKOSUKA (Hako - slang for box; Suka - skyline) which dominated the late 60's in racing in Japan, decimating the opposing Porsche 904's.
The final car to wear the GTR badge B4 the 1989 R32 GTR was the 1973 KPGC110GTR, which closed out these glory years for the skyline for nissan. Within these 16 years, Nissan truely made the skyline a Box, and left the days of inline 6's alone, FJ20's until the 180ps RB20DET powered R31 GTS 2 door model was released in 1986. The following year, 800 GTS-R's powered by 210ps RB20DET-R engines were released as the closing model for the old shape.
August 1989 saw the release of GODZILLA onto Japanese streets, and by 92 the car had taken over from the Cosworth Sierras as THE car to beat in Group A touring cars. They were subsequently banned in the Aussie Touring Car Championship the following year (due to the inability of anything to compare to it) and Nissan Australia (the only country other than Japan to formally sell the RB26DETT powered GTRs) lost a crap load of money on R32's which just sat in dealerships across Australia due their high price.
The rest of the GTR history is easily available on forums across the world (much as the stuff above could be found too) so I won't waste anymore space, but to displace the claim by Porsche that they were the first company to send a car around the Nurburgring in under 8 min's. In 1995, Kazou Simizu drove an R33 GTR around with a laptime of 7:59.8, which he cut to 7:52 in a production R34 GTR V-Spec in 1998.
And I agree with LaBounti, there is no current GTR, unless you count the one Top Secret is Building out of a G35 skyline....
http://www.topsecretjpn.com/news/newgtr.htm
Enjoy....