A group of Syrians arrives on Lesvos after sailing on an inflatable raft from Turkey. PHOTOGRAPH BY ANDREW MCCONNELL / PANOS

Samar paid five hundred dollars to cross from Turkey to the north shore of Lesvos, in Greece, on a flimsy seven-metre dinghy with her two children and sixty-two other people. When she arrived, a Belgian woman took pity on her, and drove Samar and her children to Mytilene, the capital of the island. The drive takes about an hour and a half, on winding mountain roads, and is more than forty miles. Samar was lucky. She had paid less than half what most of the refugees and migrants arriving in Greece today pay, and she didn’t have to walk across Lesvos. Although N.G.O.s and the local government have recently provided buses to transport the migrants, the buses come sporadically. As the refugee population swells, people are trapped for several days in areas where there is no shelter. Many locals won’t take refugees in their cars or taxis, citing a law that makes it illegal to transport unregistered migrants.

The day before I met Samar, aid workers had found her weeping because she could not find a tent for her children. The Syrian refugee encampment in Mytilene, Kara Tepe, on an old driving track and what appear to be ruins, has a capacity of about five hundred, but some two thousand refugees are waiting there at present. The detention center where non-Syrian refugees are held, Moria, is also overflowing, and people have been found trying to break in because the conditions in the overflow area are so squalid. Thousands of people are also camped out in the port, in a parking lot, and beneath the façades of crumbling midcentury concrete buildings. When ferries arrive in the port, refugees shelter in the shade thrown by the massive steel hulls. Some have been stuck on the island for weeks, and they have difficulties finding tickets to make it to Athens, even if they have gone through the complex process to get their transit papers.

Samar had been on the island for three days when I spoke to her, and had registered with the police for her transit papers to travel to Athens and then on to a wealthier European country. Despite the heat, she wore a neat black hijab that made her look younger than her forty-two years. She had come with her five-year-old son and four-year-old daughter, from Yarmouk, a Damascus neighborhood that was founded, in 1957, as a Palestinian refugee camp, but soon became part of the city. Samar and her husband, who are Syrian, lived there and ran a small grocery. After the Assad regime barrel-bombed Samar’s home in January, her husband told her to leave with the children. “The city was under siege and there was no food,” she told me. They crossed the northwest border of Syria into Turkey, and spent several months in a refugee camp near the border, in Kilis, before passing through Turkey to Lesvos. By April, ninety-five per cent of Yarmouk was controlled by ISIS, and Samar’s husband was trapped there. “I cried a lot. No one cried like me,” she said. “It’s not easy leaving your country, your family.”

As I was speaking to Samar, an older woman in a patterned hijab interjected. “The trip from Syria to here was more difficult than staying,” she told us. “Even though there were bombs every day, it was better for us.” She pointed to a broken leg to illustrate the point. Most of the ailments the refugees suffer come from minor wounds incurred on the journey, but, beyond a trailer operated by Doctors Without Borders and roving Médecins du Monde clinics, there is little medical care. When I visited the Doctors Without Borders trailer, a man was complaining about a pain in his head to the two medical workers and translator on duty. He had fallen into a river when he made the crossing from Syria to Turkey, and his ear had become infected. Now it was swollen and painful, and a fairly quotidian infection threatened to permanently damage his hearing.

According to the International Rescue Committee, a nonprofit that is helping to administer Kara Tepe, the refugee population of the island has swelled to about twenty thousand. By the end of July, the U.N. High Commissioner for Refugees estimated that about a hundred and twenty-four thousand refugees and migrants had arrived in Greece. The number is now closer to two hundred and eighty-eight thousand. Without funding to house, feed, and shelter the refugees, and with the ferry companies all booked with tourists (this situation has started to improve, according to an I.R.C. representative), it is difficult for the islands to provide for the refugees or to move them to the mainland. Early this month, the mayor of Lesvos, Spyros Galinos, asked the Greek government to declare a state of emergency. “The situation was critical. We could not accommodate this large number of people in a small island like Lesvos,” which previously had a population of about eighty thousand, Galinos’s press officer told me, in an e-mail.

Although the E.U. recently announced that it would provide four hundred and seventy-three million euros for assistance to the refugees, critics say that the money will not go far enough, and the funds have been released slowly because of political turmoil in Athens. Kirk Day, the International Rescue Committee emergency field director, told me that he hadn’t seen conditions this bad since he worked in an unmanaged camp in Zaire as the country plunged into civil war, in the late nineties. “The system is just not working,” he said. The main problem was that there were not enough boats to take refugees to Athens. While Day and I were speaking, he spotted the island’s deputy mayor, Giorgos Katzanos, who comes to the camps every day to try to organize services. Katzanos also insisted on the necessity of boats “immediately; otherwise we start the problems.” Last Friday, riots broke out in the port among refugees who were tired of the long wait for their transit visas. Some even set fires in the camps. The authorities have pushed to register more migrants, but they keep on arriving on Lesvos.

Greece—a country that, in its recent history, has not faced large flows of refugees—has been mixed in its reaction to the crisis. Earlier this summer, on the island of Kos, local authorities locked migrants in a stadium for almost twenty-four hours, and there have been stories of attacks on refugees, often by supporters of the neo-Nazi Golden Dawn party. Still, on Lesvos, many people I interviewed—aid workers, volunteers, local officials, and the refugees themselves—spoke of the kindness the Greeks had displayed. Anna Halford, a coördinator for Doctors Without Borders, remembered a recent day when she visited the Moria overflow area and saw a local man standing next to his car. “He had the look of someone who didn’t know what to do. He took me by my coat and said, ‘I have brought figs from my garden, but I think there are more people than there are figs.’ I said that was O.K., but he said, ‘What if people fight over them?’ I told him that nobody would fight, and we all shared out a box of big, beautiful figs,” she recalled.