Counterfeits are sometimes seen as a sign of success. They show that your business is doing well enough for someone to bother copying it. However, once the initial flash of pride is over, the reality of having someone not only cashing in on years of hard work but also damaging the brand's reputation starts to sink in.
Counterfeits, knock offs and close copies are all closely related and cause varying degrees of headaches. The amount of money at stake can potentially be huge. For example, Nike recently shut down a counterfeiting ring in New York where the counterfeiters had so many fake Nike Air Jordans that, if they were genuine, they had a retail value of USv$73 million.
Typically counterfeits infringe at least copyright and trade marks but in Europe designs can also be very helpful, particularly registered designs which, as they are a registered right, can be useful in terms of persuading online platforms to remove goods. (Watch out though, in some countries, such as Germany if the design is likely invalid, it can leave your open to an unfair competition claim.)
There are lots of tools for monitoring counterfeits online from those provided by the various e-commerce and social media platforms themselves e.g. eBay's VeRO programme to third party vendors who manage the whole or part of the process.
One of the big current counterfeiting challenges concerns closed social media groups which can involved large sales of counterfeits but are hard to monitor and where social media companies are typically reluctant (or unable) to provide any insight into the group itself. Investigation is still your best bet for the early intelligence gathering stage and as people are often less discreet when they believe they are shielded from the public eye, it can be very fruitful. The downside is that it is time consuming and fairly expensive to investigate.
Counterfeiting is both a civil and a criminal offence in Europe. Different countries take a slightly different line as far as the criminal side is concerned. Broadly speaking, it is easier to convince the authorities in southern European countries such as France, Spain, Italy etc that they should take criminal enforcement action.