It is possible to construct underground tunnels. Using the Tab key, you can swap views between ground and tunnels.

There are four different types of tunnel and each of them has sixteen wall types which can be used freely. 

To be able to enter such tunnels during the game you need to place an entrance on the map (right above the tunnel)

Tunnel width can be adjusted with a brush.

All tunnels can be displayed on the map when pressing the 
„Show on surface” button.