Some people have a dispute with AT&T. They had to pay sales tax on ostensibly free phones, so they claimed a dispute and according to the AT&T service contracts were forced to subject themselves to third party arbitration. However, AT&Ts contract additionally stipulates that they may not be rolled into a class arbitration. In other words, every arbitration with AT&T must be one wronged party v. AT&T. Clearly this is in AT&Ts favor as they can go about intimidating, avoiding, and inconveniencing the majority of claimants out of bothering to pursue arbitration. They are assisted in this endeavor by piles of legalese, and also by the small size of each individual claim ($30 in this case). The state of California in its wisdom wrote a law invalidating such clauses precisely because they allow a large company to defraud large numbers of people out of small amounts of money without much chance of ever getting in trouble for it.
The 5 justices that made this ridiculous ruling seem to have based it on the idea that California's law goes against the FAA. Their ruling is in the first link of this post. It says that the FAA allows state laws to supersede it only if they are consistent with the intent of the bill (which is to put arbitration agreements on the same footing as all other contracts). They basically say that since California's law specifically targets arbitration agreements it is contrary to the intent of the FAA and therefore it is not upheld. They are all wrong.
The 4 justices who dissented in this one have it exactly right in my view. They are in the second half of the first link of this post. Basically they say: If you have to hire a lawyer to file a claim, or even spend a lot of time and effort or have any sort of expertise, and the amount of money in question is small, then no one will ever file claim, and the bad company will get away with its bad practices forever. This is obvious. They also point out a delicious and hilarious number of flaws in the majority opinion. This rather undermines their final words: With respect, I dissent.