What does need to be finished is the London-to-Ashland corridor. KY 30 from Tyner to Levi, KY 11 from Levi to Beattyville, KY 715 from Zachariah to Pine Ridge, and KY 7 from north of West Liberty to Sandy Hook and a short section near Grayson Lake. Part of KY 7 in Elliott County is now under construction.
Major gravedig and arguably off topic, but I feel like writing about what I've found messing around with Google Maps in eastern Kentucky.
I Googled London to Ashland, and this route came up as the second choice behind I-75, KY 627, and I-64. It's currently 28 minutes longer but 13 miles shorter. Not bad. The average speed is over 50mph compared to 62 on the Interstates+ route, which also really isn't bad. When the improvements that HB mentioned are done, the route might be of equal merit to the 75-627-64 route, despite that probably not being an explicit goal of the project.
Oh: According to Google, new KY 30 from near KY 847 to KY 11 at Levi is open. That's 5.4 miles.
I also checked Lexington to Wytheville, VA. The Interstates are the quickest way, but the second choice is KY 15 through Hazard, then US 23 and US 58 Alt. to I-81. the KY 15 route is about 20minutes longer, but 20 miles shorter, and of course avoids the tolls on the WV Turnpike. KY 15 looks squiggly on the map, but a lot of it has been improved over the years. The average speed on KY 15 from Jackson to Pound Gap is 49mph, compared to 55mph on the whole route, including 110 miles on Interstates and Mountain Parkway.
So, freeways, expressways and APD-type highways aren't everything. Not everything worth building looks good on a map.