The conservation group WWF is calling on European consumers to make careful choices in the fish they buy and eat.
The report draws attention to fishing techniques
A WWF report says much of the fish sold in Europe is the product of illegal, destructive or wasteful fishing.
The report warns that continuing to buy it will bring many fish stocks to the brink of extinction.
One of the main casualties is plaice. The report says about half the plaice caught are too small and are thrown back - by which time most are dying.
Justin Woolford, of the WWF's European fisheries campaign, says such a buoyant market encourages unsustainable fishing practices.
"We've got too many boats chasing too few fish - there's a lot of illegal fishing going on as well," he said.
The report also draws attention to illegal drift-net fishing for swordfish, which it says kills an estimated 100,000 sharks every year - two for every swordfish.
The WWF says consumers should only be buying fish with a Marine Stewardship Council label, which certifies that the fish bearing it has come from a sustainable and well-managed fishery.
Some European retailers have begun using the label.
The EU has restricted fishing in European waters in recent years, in an attempt to preserve fish stocks.
In July, the European Commission proposed a 15% cut in quotas on cod fishing in the Baltic Sea.