In 1903 the first commercial batch of decaf was brewed in Europe by steaming the coffee beans in a salt water batch and then adding benzene producing decaffeinated coffee.  Kaffee Handels-Aktien-Gesellshaft (Kaffee HAG) was known as Coffee Trading Company throughout most of Europe.  France sold it Café Sanka and in the US it was known simply as Sanka.  This process, know as Roselius is no longer used as it was considered to be a health hazard.  Cafe HAG and Sanka process it in a healthier way now.

The triglygeride process uses hot water and a coffee solution to draw the caffeine out and the beans are then transferred to a container to soak in coffee oils made from used grounds.  The triglycerides in the oil remove the caffeine leaving the flavor and the beans are then dried.

The CO2 process, also known as supercritical fluid extraction, pre-steams beans which are then pressurized and soaked in supercritical carbon dioxide for 10 hours.  The pressure is released and the CO2 evaporates.  Alternatively the pressurized CO2 is filtered through charcoal or water filters.

Even though a coffee claims to be decaffeinated some caffeine remains, and if you are a heavy coffee drinker (5-10 cups a day) that would equate to drinking one or two cups of coffee with caffeine.