If clean, simple joinery is required, welded joints may be appropriate. Three very different versions exist: electrically welded, the more traditional fire welded and gas welded.
Another option is to use discreetly hidden dowels, pins, or other mechanical fasteners but care is always taken to try to avoid using visible nuts and bolts wherever possible ... unless they are part of the design.
Alternatively, more creative joinery can be used as an expressive design feature in its own right. Verdigris' blacksmith, David Hyde, has a large repertoire of techniques he can call on; a selection of these is discussed below.