There are two ways it can be done, but only one it is really done on industrial scale.
The old way was that you could pre-brew the coffee for a few seconds. Large portion of caffeine extracts *very* fast. If you then remove the coffee and move it to fresh water, the resulting coffee will have significantly less caffeine and still taste like a weak coffee.
Caffeine sensitive people still do this with [tea](https://www.thespruceeats.com/how-to-naturally-decaffeinate-tea-765280). But I have never heard anyone actually doing it with coffee after industrial decaf became a thing.
These days, on industrial scale, they flush the coffee with a solvent, like alcohol / acetone or compressed CO2. The CO2 extraction being the latest and greatest. It binds the caffeine, but little else. When you then remove the solvent, you’re left with coffee with less caffeine.
The beans are submerged in “supercritical” carbon dioxide. A supercritical fluid is a state of matter with both the properties of a liquid and a gas. The liquid property of the fluid allows substances to be dissolved in it (in this case the caffeine), the gas like properties of the fluid allow it to fully permeate the beans, extracting caffeine from within.
If the carbon dioxide was in normal liquid state it would only touch the outside of the bean, so only the surface level caffeine would be extracted
The process is either chemical or by water, which is well explained above, but I will add that the longer a bean roasts, the more of the caffeinated oil seeps out, the less caffeinated it is! So light roasts have more caffeine than dark roasts! Fun little factoid not everyone knows. And yes the caffeine is captured and does go into sodas and other things. Source: coffee industry for 13ish years
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