But who are the 10 athletes in the Refugee Olympic Team? What are their stories? And how are they doing in Rio?
Rami Anis (swimming)
Who is he? The 25-year-old fled war-torn Syria in 2015, travelling by boat across the Mediterranean Sea to Turkey before continuing to Belgium.
How did he do? Anis earned a standing ovation after setting a personal best in the men's 100m freestyle. He clocked 54.25 seconds to finish 56th out of 59 in the heats.
What did he say? "It's a wonderful feeling to compete in the Olympics. I don't want to wake up from this dream."
When is he competing next? On Thursday, in the men's 100m butterfly heats (18:16 BST).
Who is he? The "lost" South Sudanese runner lived in a refugee camp in Kenya for 10 years after escaping a civil war. He started running competitively just over a year ago, but despite the weather being unfavourable for training during the day, and there being no facilities, he continues to compete.
When is he competing? Friday, 12 August, in the men's 800m heats (12:10 BST)
What has he said? "Sport gave me a sense of belonging. Even if I don't get gold or silver, I will show the world that, as a refugee, you can do something."
James Chiengjiek (athletics)
Who is he? Like many of the "lost boys of Sudan" who fled to refugee camps in Kenya known for its long distance runners, James Chiengijek fled his home to avoid being recruited as a child solider. But the injuries of having the wrong footwear never stopped him, as he aims to help others like himself.
When is he competing? Sunday, 14 August, in the men's 400m heats (02:00 BST)
What has he said? "My dream is to get good results at the Olympics and also to help people. Because I have been supported by someone, I also want to support someone."
Paulo Amotun Lokoro (athletics)
Who is he? Paulo Lokoro was a cattle herder in South Sudan, until the war broke out and he fled to join his parents in Kenya. On the journey there was only fruit to eat, and when he arrived at the refugee camp he did not even have any shoes.
When is he competing? Tuesday, 16 August, in the men's 1500m heats (14:30 BST)
What has he said? "A dream would be to break a record. To win a medal, a gold, that is my dream."
Anjelina Nadai Lohalith (athletics)
Who is she? Since the age of six, Anjelina Lohalith has been disconnected from her family in South Sudan after escaping civil war. The 21-year-old hopes her running career will allow her to help improve the life of her family, return one day and help her father build a better house.
When is she competing? Saturday, 13 August, in the women's 1500m heats (00:30 BST)
What has she said? "I'm happy because it will be the first time refugees are represented in the Olympics. It will inspire other refugees because wherever they are they will see that they are not just the 'other people'."
Rose Nathike Lokonyen (athletics)
Who is she? Rose Lokonyen has a natural talent for running, and only discovered it at a 10km competition at her refugee camp in Kenya where she came second. She only started running with shoes last year. The South Sudanese runner believes she would have died if she and her family had not fled the country when she was 10.
When is she competing? Wednesday, 17 August, in the women's 800m heats (14:55 BST)
What has she said? "My dream, my first priority, is to help my parents and my siblings and then after that to help my fellow refugees."
Yonas Kinde (marathon)
Who is he? The Ethiopian marathon runner had to leave his native country for political problems, and has been living in Luxembourg since 2013. He has a marathon time of two hours 17 minutes and would qualify for the Olympic team if he had his citizenship.
When is he competing? Sunday, 21 August, in the men's marathon (13:30 BST)
What has he said? "I can't explain the feeling, it has power, it's amazing. It's very good news for refugee athletes that Olympic Solidarity have given us this chance to participate here."
Yolande Mabika (judo)
Who is she? Yolande Mabika fled the Democratic Republic of Congo three years ago to live in Rio after so much suffering in the civil war. She was separated from her family at a very young age and remembers running alone and being picked up by a helicopter and taken to the country's capital. She was then taken to a centre for displaced children where she took up judo.
How has she done? She was knocked out in the first round of the -70kg contest by Israel's Linda Bolder.
What has she said? "Judo never gave me money, but it gave me a strong heart. I got separated from my family and used to cry a lot. I started judo to have a better life."
Yusra Mardini (swimming)
Who is she? Mardini is known for rescuing 20 people in a boat from capsizing after fleeing Damascus from the conflict in Syria. She used her talent in open water swimming to swim for three hours and help everybody survive the journey to Germany.
How has she done? She won her women's 100m butterfly heat, but her time was not quick enough for her to progress. She also failed to progress in the 100m freestyle.
What has she said? "I want everyone to think refugees are normal people who had their homelands and lost them, not because they wanted to run away and be refugees."
Popole Misenga (judo)
Who is he? Misenga sought asylum in Brazil in 2013 after escaping the conflict in the Democratic Republic of the Congo. He was taken to the country's capital after being found wandering in the rainforest when he was six years old following his mother's murder.
How has he done? Popole Misenga beat India's Avtar Singh in his opening match, but lost by ippon to South Korea's Gwak Dong-han.
What has he said? "I have two brothers and I haven't seen them, I don't know how they look any more because we were separated since we were small. So I send hugs and kisses to my brothers."