There are a number of fuels used for barbecue - if using wood, briquettes, or lump charcoal, it is recommended that you use paper, paper with a chimney, or wax fire starters and not liquid charcoal lighter as these often impart a chemical taste to the end result.
Gas/Propane - probably the most popular fuel today is propane due to its convenience. Permanent natural gas grills where popular in the 60’s and 70’s but not often seen these days except in expensive outdoor kitchens or commercial applications such as restaurants. While gas doesn’t provide the smoky flavor, that can be achieved on gas grills, and they still provide flame for perfect grill marks and a nice crust/bark.
Wood - the oldest and most traditional way to cook meat, wood is abundant and widely available. Still used in many commercial BBQ joints, and campfires. There is nothing quite like cooking over an oak, hickory, or mesquite fire.
Charcoal Briquettes - Briquettes are natural wood remnants that are compressed and often contain binders to create the stable rounded/square shape we are all familiar with. Banned by most purists, one the most famous BBQ joints on the planet, Rendezvous in Memphis, TN uses charcoal briquettes exclusively and no smoking wood, and you can’t argue with their results!
Briquettes can be made from most any would and often contain other compounds such as starch, wax, and borax. If you use briquettes make sure there are no glues or binders and avoid the self-lighting charcoal. While convenient, it can affect the taste of the food due to the flammable chemicals and also tends to create a lot of ash that sticks to the meat.
Lump Charcoal - lump charcoal is the most natural fuel source next to true wood, which most backyard cooking devices won’t accept due to size, and dry wood is not always easily available and often destined to the fireplace. Now plentiful and no more expensive than a quality briquette, lump creates a nice crackle that adds to the fun, and is an ideal alternative to the more widely known briquettes. Lump charcoal is usually charred oak. Lump charcoal can burn as hot as 1000 degrees, perfect for searing steak, while briquettes will reach only about 650 degrees under ideal conditions.
Pellets - the latest in technology, pellets are pure, natural, compressed sawdust with no chemicals or fillers, and come in a variety of wood varieties. Pellets can be used on any grill or smoker, but were designed with pellet smokers in mind to provide a means for constant feeding of fuel to the fire.
Electric - not much to be said here - heating elements similar to those found on electric stoves and ovens provide the heat for cooking.