So right now there are many caves scattered around the map. I think that all the caves should be interconnected by an underground network. However, you should NOT be able to build in the caves. This should be used mainly for transportation.
Edit: Also, it would be cool if you could find some loot down there, maybe like an underground rad. And there should be rad wolfs and bears (or some other creatures) stalking the tunnels. Tunnels also need to be dark (duh) and it should be pretty cold down there (esp at night). However there should be some natural lighting and heat in some areas maybe from geothermal hotspots. Also, you should be able to place lanterns and camp fires in the tunnels to warm you up.
Note: I do not want tunnels to become the main focus of this game. Rust is, and will always be, about the over-world. Thats why I suggested that you cannot build in the tunnels. And it should also be a hostile place if you arnt well armed and well dressed. The tunnels should mainly be used for transportation.