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Fuel-based lighting refers to methods of lighting that only use direct consumption of biofuel. In this article, we'll focus mainly on portable fires. These are devices intented for lighting as well as carrying a fire from one place to another. Portable fires include oil lamps/lanterns, gas lamp/lanterns, torches, candles, ...
Types of portable fire
A candle uses solid biofuel to burn. It consists of a wick and a wax (ie paraffin wax, bees wax, ...).
The oil lamp uses liquid biofuel. It is the most recent type of lighting. It is made by combining a plant oil with a wick. The wick itself does not burn, but the oil does, being sucked up through capillary action by the wick.
The commercial lamp oil sold today is a substance made by refining petroleum (kerosine or paraffin oil). This is reported to generate even less smoke than (most) plant oils, but then again can not be easily made locally, nor environmentally-friendly. 
The gas lantern uses a densified (compressed) gas in a gas tank.
Portable fires are always made in such a way that they do not burn optimally. This is done to reduce the rate at which the burnable material (ie oil, wood, ...) is consumed. This however also sets limitations to the cleanliness of the burn (reducing the burn rate often creates a burn with a lot of smoke).
The reducing of the rate of burn can for example be done by integrating green plant matter (ie moss, ..) in a torch, or by simply using a less burnable fuel (ie greasier fuels). Also, for example in oil lamps, it is possible to combine a regular oil with a greasy substance (ie soap/tallow/wax, ...), or resin/pitch or animal blood, ...  The use of an acid (lye) within the oil-grease mixture may allow allow less-burnable oils (thinning effect). By combining extra substances with the main fuel (oil), the substance is now, besides being thick also stickier, for example allowing to quickly light a newly constructed fire (bundle of wood).