Although OpenSeadragon provides default buttons which are overlaid on the viewport, there are many use cases where the presentation may require a more traditional toolbar. OpenSeadragon allows you to easily dock your controls inside any element on the page.
In addition, the toolbar has logic which supports transitions between full-screen and normal mode. The user can style the toolbar in full-screen mode, including hiding it, even though it's not otherwise related to the viewer DOM.
OpenSeadragon({
...
toolbar: "toolbarDiv",
...
});