You don’t need a chimney. But if you’re relying upon combustion to stay warm, a chimney has many advantages. Smoke is mostly drawn up and out of the actual living area. You can use flammable roof materials like thatch without worrying about setting it on fire. And a chimney with a little height creates an updraft that helps the fire burn well, which aids cooking and baking. Until the invention of the enclosed stove this was the most important leap in heating.
The most important and natural addition to a chimney is the cap. Rain or snow coming down the chimney is annoying, and may put out your fire. In the US the design of chimneys and their caps are often standardized, dictated by local building codes. But in freewheeling Europe, there’s a huge range of these things! The one at the top of this post is practically a young house, sloping stone roof and windows all complete.
The two in this picture seem to be made out of the same terra cotta roof tile as their parent roofs. Just lean a couple tiles against each other and secure them with some cement. This simple notion can evolve into something pretty elaborate. Four, five, eight tiles, why be shy?
Finally there’s this little elaboration. I can’t quite discern whether this is attached to the chimney cap or just balanced on up there. Surely it’s affixed in some way, otherwise a passing pigeon or a vigorous gust of wind would knock it over? Adding a weight on top of your chimney cap helps it to stay on.