Skirting corporate taxes is getting pretty unpopular these days. Just ask Apple.

The world’s most valuable company is coming under fire from the European Union for funneling the lion’s share of its international sales through subsidiaries in Ireland to save money on taxes. Authorities across the pond are investigating the legality of Apple’s scheme and considering whether to make the company pay back taxes.

But can they? And what exactly is Apple doing wrong? For answers to these and other burning questions, here is a breakdown of the Apple tax saga:

Q: What in the world do Apple and Ireland have to do with each other?

A: Back in 1991, and again in 2007, Apple struck tax deals in Ireland that allowed the company to use two of its Irish subsidiaries — Apple Operations International and Apple Sales International — as shelters for its foreign profits. Neither of those units had employees in the country, and that raised suspicions.

But considering that Ireland’s corporate tax rate is 12.5 percent, roughly a third of the tax rate of other European countries, people figured Apple was trying to take advantage of the tax benefit.

Q: Why does the EU care about this?

A: The executive commission of the 28-nation bloc is concerned that the tax treatment Ireland granted Apple “constitutes state aid,” which would run counter to EU law. Countries in the EU are not allowed to help individual companies avoid free-market competition. And they are certainly not allowed to grant companies special deals that are not available to other firms. As a result, the commission has been sniffing around Apple’s tax deals with Ireland since June.

Q: June, you say? So why is everyone talking about this now?

A: On Tuesday, the commission made public a report and a letter that it had sent to the Irish government, spelling out the problems authorities found with the tax deals.

A prime concern was the way Ireland let Apple calculate transfer pricing, or arrangements that involve moving profits and losses between subsidiaries in different tax jurisdictions. Typically, companies label those profits and losses as internal corporate payments for goods or royalties. The commission thinks Apple exaggerated the transfer pricing by inflating the price for goods to shift profits to Ireland.

The commission said the tax deals Ireland struck with Apple in 1991 and in 2007 have “several inconsistencies” that may not comply with international taxation standards. It argued that, compared with other EU countries, the deals lasted much longer, which translates into an unfair tax advantage just for Apple.

The EU is none too pleased that Apple’s applicable tax rate seems to be the result of “a negotiation rather than a pricing methodology” that a “prudent, independent” tax authority should have rejected, according to the report.

Q: Okay, but how much money is Apple saving with these deals?

A: Well, the commission estimates that the company avoided at least $3.5 billion in US federal taxes in 2011 and $9 billion in 2012.

Apple said in its latest June earnings report that it had $164 billion in cash, with $138 billion tucked away in foreign subsidiaries. The company said its effective US tax rate hovers around 26 percent, lower than the US corporate rate of 35 percent, because of the foreign earnings.

In its quarterly filing, Apple said its Irish subsidiaries generated “a substantial portion” of those foreign earnings.

Q: So, what can the EU do about this?

A: The EU has the authority to order Ireland to collect back taxes from Apple. It’s unknown exactly how much Apple could have to pay, but some analysts say it could be hundreds of millions of dollars.

Q: What’s Apple got to say about all of this?

A: Apple insists it has not received any favorable treatment in Ireland. In a statement, the company said, “We’re subject to the same tax laws as the countless other companies who do business in Ireland.”

Apple noted that its tax payments to Ireland grew tenfold since it launched the first iPhone in 2007. Still, the company agreed that “comprehensive corporate tax reform is badly needed” for the international market.

Q: Okay, so Apple found a way to cut its tax bill. What’s the big deal? Don’t most companies do the same things?

A: Yes, it is pretty common and legal for multinational corporations to use foreign operations to avoid US taxes. There are a whole host of companies that even move their headquarters oversees to lower their tax bills, a practice known as an inversion.

If the term “inversion” sounds familiar to you, it’s probably because the Obama administration recently issued rules to make it harder for US firms to bring cash earned abroad back home tax-free. The rules won’t block the practice. For that to happen, Congress would need to change the tax law.