The European Union dodged an imminent trade war with the US this week, but markets and a growing chorus of critics have dispelled early hopes that the deal will bring a sense of stability back to transatlantic relations.

Both sides hailed the agreement as the biggest ever. But it will come at a cost to the European Union, and many details have yet to be nailed down.

"I think it's the biggest deal ever made," Trump said of the new agreement, which will reduce the bloc's tariff rate to 15 percent.