When Polish photographer Rafał Milach took these pictures, on the eastern border of his country, the war in Ukraine was less than a week old. During this week, nearly a million people have fled Ukraine, including half a million to Poland. (Both numbers have since doubled.) It was very cold along the border. Before the refugees crossed to safety, they endured delays of hours or even days: by car, by train, on foot. The first quality that emerges from these portraits is the exhaustion of the faces. The muted colors in the background – the tin sky, the dull pastel walls, the dead white of the bus – seem to sympathize.

I saw Milach at work and was struck by how long he spent talking with each refugee before taking a photo. He wanted to hear their stories. “What can you do when a grown man starts crying in front of you? ” he told me. “What can you do when people tell you that they had to leave their homes and loved ones overnight? I can listen. I can document it – to remember it, so that the images and words can resonate long after this nightmare is over.

Despite the heartbreaking situation, these photographs are full of life. There is sadness in them, but also defiance. The man in the blue jacket is Sher Alkroi, a Syrian citizen. He left his native country in 1996 and ended up in Ukraine, where he owns a furniture business. Alkroi fled his home in Kharkiv near the Russian border when the fighting started. He told Milach, “We didn’t take anything – the kids, that’s all. We didn’t take any money – the banks were closing, we couldn’t withdraw money, our money was left in the office. We have nothing, we left. We only have enough money for gas.

What will Alkroi do next? He did not know. Maybe he would go to Germany, maybe Norway. All he wanted was peace. In Syria, he noted, “there is also a war”.

Mobile phones feature on several plans. We are all attached to our devices, but the refugees I have met have clung to them, as they are a lifeline for news from home and for ideas of where to go next. If the exodus from the war in Ukraine sometimes looks like a crisis torn from the pages of 20th century history, it is also a resolutely modern crisis. Refugees continually consume social media content about the conflict they are fleeing. They navigate their upheaval using Telegram channels that tell them where the shortest lines are, which agencies could help them, or how to get a bed for the night. Technology allows them to share advice, support and love in real time.

I was not surprised to see pets at the border, as well as other cuddly animals. A Ukrainian medical student I met at a Polish train station told me that, in her haste, she had packed only one non-essential item: a teddy bear. Many children seem to have had the same idea. Milach’s photograph of a girl clutching a giant stuffed shark while her anxious, troubled-eyed mother makes a call captures the essence of the refugee experience: ordinary people, their lives violently turned upside down, clinging to the comfort.

The mother on the phone, Maryna Klimova, told Milach that she planned to return to Ukraine alone and join the resistance. “I’m here because of her,” she said of her daughter, who is 11. “My daughter comes first. But when she’s safe, I can help her. Klimova knew “a very safe space for my child in Munich”. Then she came back “to help our people, they need a lot of help”. Klimova is an actor. If not for the Russian invasion, she says, she would now be in Kiev, in a theater on the left bank of the Dnieper, performing in a staging of Homer’s Odyssey.

—Ed Caesar