Oil lamps used thousands of years ago were fueled by specific oils produced in specific locations. Mediterranean cities commonly used olive oil, and coastal cities in Asia and around Europe used fish oil, whale oil and the oil from nuts. These fuels worked well and provided light but were very high-polluting and put out a lot of smoke. Whale oil became the oil of choice later on as it was the cleanest burning oil for this type of lamp.
Today, the most common types of lamp oils are petroleum based. Kerosene is common but is fairly high polluting, so many stores carry scented lamp oils that have the words "ultrapure" or "ultraclean" on the label. The "ultra" oils burn cleanly, and you can use them in classic oil lamps as well as lanterns.
Using colored lamp oils is popular for a couple different reasons. The color enhances the way the oil lamp looks, especially if it's made of a transparent or translucent material. You can turn an oil lamp into an attractive piece of art when you keep it on a shelf in your home. The colors, made from various dyes, have no impact on how well the oil burns or how many byproducts it produces as it burns.
Scented lamp oils are extremely popular and come in hundreds of different scents. Vanilla and lavender are scents that have a calming aromatherapy aspect to them and can help your home smell good. The oil lamp gives off a warm and comforting light. It's common practice to use seasonal scents with them, such as pine or gingerbread, for the holidays.
Never use oil lamps in an area with no ventilation. This could lead to carbon monoxide poisoning and that can kill you. Read the instructions that came with your oil lamp to ensure you are using and maintaining it properly.