A woman crouches down in the doorway of a blue and yellow train at a station in Kyiv, Ukraine's embattled capital city. Her husband stands on the platform below and cranes his neck up for a kiss that both hope will not be their last.

As the train door closes, the woman holds up their 2-year-old son and he smiles and presses his tiny hand against the smudged window to wave goodbye to his father, who is staying behind to fight the Russian invaders.

Nearby, a grandmother reaches out to bid farewell to her daughter and grandson, who are on the train headed toward the border with Poland. She backs toward a wall of the train station and is soon overcome with emotion. She places her hands over her mouth, squeezes her eyes shut tight and lets the tears fall.

These are the goodbyes that have been repeated across Ukraine in the week since Russia invaded and began pounding the country's cities with bombs. The UN says the fighting has sent more than 1 million people fleeing the country, a number that is already the swiftest exodus of refugees this century and one that could soon skyrocket even further.

Those leaving are overwhelmingly women and children. Ukrainian men have been ordered to stay and fight in the war.

At the train station in Kyiv crowds of people carrying luggage stand in the cold as they wait for their chance to board a train. Mothers hold children bundled in winter jackets and stocking caps, some clutching onto stuffed animals. Men help the elderly get to the train, even using a luggage cart to carry one woman with crutches.

Up and down the platform there are tearful embraces.

Once on the train, many of those leaving press their faces against the windows for a last glimpse at those staying behind. One woman reaches her hand out the door for a fleeting brush of a loved one's cheek.