This is a strange one. According to the good folks over at Tom's Hardware, the DisplayPorts on both the Nvidia GeForce GTX 1080 and GeForce GTX 1070 are incompatible with the HTC Vive headset.
The HTC Vive has two options for connecting your graphics card to the headset through the HMD's link box: HDMI or mini-DisplayPort. Most people will end up using the HDMI connection as it's more common and a HDMI cable is included in the box, but DisplayPort is there for those who have already used the HDMI port on their graphics card for another display.
When hooking up a GTX 1070 or GTX 1080 to the Vive through DisplayPort, Tom's Hardware reports that SteamVR does not detect the headset. The headset works fine through HDMI, but not through DisplayPort on both the latest drivers and the drivers that launched with either card.
This is an unusual issue for Nvidia and something that has clearly slipped through the cracks during testing. It's not clear whether the problem can be addressed through a software update, and the only word that's come from Nvidia since the issue first surfaced is that they're "still investigating the issue".
And it's not like this issue is found in all Nvidia graphics cards: you can connect a GeForce GTX 980 Ti to a HTC Vive through DisplayPort and it works just fine. It's just 10-series cards that are experiencing the issue, so hopefully Nvidia can identify and resolve this problem in the near future.