A company issues an invoice for non-existent goods and then exchanges it with another company's invoice for non-existent goods and then both sides somwehow collect VAT on the non-existent transaction.
Yes, it's a huge problem in the EU, and it's caused by the idiotic way that VAT rates are not harmonised across the EU. The logical thing would be for a single EU VAT rate, set at the average of the current 28 rates. But because member states are idiots, we have the situation that the VAT system is wide open for abuse.
This article explains it, but it's a bit technical - en.wikipedia.org/wiki/Missing_trader_fraud
PO started working on this, and PiS should finish the job - en.wikipedia.org/wiki/SAF-T - which essentially makes the job of the tax office much easier. The estimate I've seen suggests 15-16 billion złoty will be saved when the system comes into full use in 2018. Essentially, it means that businesses have to provide financial data in a set format - that the tax office can then use standardised tools to spot potential frauds. For instance - anyone importing small, high value items (let's say mobile phones) will have to also supply sales invoices. Let's say that in the tax office, an inspector notices that some new company in Lublin started up and bought 2 million złoty worth of mobile phones. The system doesn't find any evidence of sales to customers, but rather the phones were sold to a company in Poznań. The inspector can then check the Poznań company - and if the phones were then sold to someone in Germany, it's highly likely that there's VAT fraud going on.
PO closed a lot of the common frauds, such as steel and electronics. The problem with the new PiS VAT law was that there were several very bad ideas - for instance, businesses would no longer be able to apply for binding rulings on VAT issues. The law also introduced liability for businesses that might have had no idea that they were part of a scam - which was madness.
Personally, I think PiS could do very well by introducing an always-online system. There's no reason why there can't be a permanent data connection between the kasa fiskalna and the tax office - likewise, no reason why companies issuing fatkury can't automatically transmit them to the tax office. It's a lot of work in the beginning, but it would mean that the tax office has all the relevant information instantly. It would be nearly impossible to commit fraud in this case, because systems could be set up to alert inspectors instantly of suspicious behaviour.