After the oil price shocks of the late 70's and early 80's, experimenters began to figure out a way to make thick vegetable oil slip through modern injectors and injection pumps that had become optimized for lighter petrodiesel. By combining alcohol with vegetable oil in the presence of an alkaline catalyst and low-grade heat, the three fatty acids in the triglycerides that make up vegetable oil split apart, and the viscosity is reduced to something similar to petrodiesel fuel. Glycerine sinks to the bottom, and can be used as a natural detergent, or for soapmaking.
Biodiesel can be used in nearly any diesel engine, without any engine conversion. However, biodiesel is a stronger solvent than petrodiesel -- so much so that it will not only "clean out" the fuel tank, sending debris into the fuel filter, but it will also soften and dissolve many rubber and plastic products, including those used in fuel lines and pumps in older vehicles. This deterioration can take years, however, and the replacement of rubber components doesn't have to happen immediately.
Biodiesel features much lower pollution than petrodiesel, in almost all aspects. It is naturally oxygenated, which means that it burns more completely, which is particularly effective in reducing the pollutants of most concern to those with breathing problems: unburnt hydrocarbons and particulates. However, this oxygenation also results in higher combustion temperatures, which results in slightly elevated oxides of nitrogen, a component of photochemical smog.
Another big advantage is carbon dioxide emissions, which cause global climate change. Because vegetable oil comes from plants that consumed carbon dioxide last year, rather than millions of years ago, as is the case with petrodiesel, it can be described as carbon-neutral.
However, most commercial biodiesel is made with methanol, which could be made from biomass, but is currently made from natural gas, a fossil fuel, so that portion of biodiesel does produce a net increase in greenhouse gas. Also, commercial biodiesel is produced from crops that were factory-farmed using large amounts of petroleum products for farm machinery fuel, fertilizer, and insecticide.
Also, biodiesel has a slightly lower energy content than petrodiesel -- 5% to 10% lower. In typical use, this is barely noticeable, but in low powered vehicles, it makes a difference.
One other disadvantage is that biodiesel typically has a higher gel point, the temperature at which waxes begin to solidify. This results in waxing the filter, or temporarily clogging the fuel filter, at temperatures as high as a bit above freezing. This can be remedied by cutting the biodiesel with 25% to 75% petrodiesel -- at least until the temperature warms up!