Wavy edge siding is a cool way to incorporate a unique, rustic look to a project. We are designing a home right now where we are using some wavy siding on the exterior above a stucco application and the planks we picked up are amazing (above).
Wavy edge siding can be painted (example above around dormer windows) or left natural depending on the species of the wood. These examples (below) from my finish carpenter are left natural and are walnut.
The process of milling the wavy edge is pretty crazy. The natural log edge of the board is left on after cutting the wood into planks and the result is a wavy edge along the sides of each piece.
Here is a good video about the installation of wavy edge siding. Just ignore the video if you are bored, but it is still a great video for anyone who, like me, finds any sort of install interesting.