If you owned old kitchen appliances or old computer you might notice that they the once cream white plastic become increasingly yellow, old and disgusting. I have read that UV lighting can damage plastics as they disrupt the structure of plastics but what really is at play here? What chemical reactions are happening? Are such damages reversible?
What you're specifically describing is typically known as UV degradation. The color change is due to the oxidation of the polymers that make up the plastic. These chemical reactions are demonstrated in satisfying detail here. Under the section titled "Photodegradation" is where you can find the intricacies of the polymer-oxidation process. And yes, such damages are reversible. As you will read, the oxidation process results in the formation of free radicals, which are "atoms or groups of atoms with an odd (unpaired) number of electrons," to quote Wikipedia's definition. The formation of these radicals is the reason for the color change (since certain light gets reflected because of these new molecules, in many cases yellow light, etc...)
To get rid of the radicals, you can add hydrogen peroxide, which allows hydrogen to bond with the radical (hydrogen has an additional electron), thus de-yellowing the plastic. This is demonstrated here.
As a further note, UV degradation is not the only process that makes plastics turn yellow, as you will probably read in that paper. There are also processes like biodegradation and mechanical degradation that are similar to photodegradation but still have their own cool processes.
Your initial question was "What makes ABS plastic turn yellow." I should point out that the first few words of the second link read "Manufacturers add bromine to ABS plastic to act as flame retardant. Over time, those chemicals react to the plastic's basic polymers and turn yellow." Ergo, there is probably more to the yellowing of ABS plastic in particular than just photodegradation.
Lastly, I should point out that the yellowing of plastic needn't happen in the presence of oxygen. But again, that is addressed beautifully in the paper.