More than 500,000 people have already fled Ukraine, according to the United Nations – their long journeys made even more traumatic by the freezing temperatures.
This has meant families separating too, with men of fighting age not allowed to leave Ukraine, and thus leaving their wives and children at the border – so that they can take up arms.
Tens of thousands of refugees have now crossed into Hungary – our correspondent Paraic O’Brien is in the Hungarian border town of Zahony.