More than 1.3 million people have fled Ukraine since Russia’s invasion began.
Families have been torn apart as women and children are given priority at congested border crossings.
Many Ukrainian men – father, brothers and husbands between 18 and 60 who are of fighting age – have been urged to stay behind and defend their country.
Some women are leaving their children at the border to return home and protect their country with their husbands, the UN refugee agency (UNHCR) said.
This could become the “biggest refugee crisis this century”, the UN has said, predicting that as many as four million people could leave.
Who is leaving?
“It is women, children and the elderly that have been escaping and seeking protection with literally only small pieces of luggage and the clothes on their backs,” Christine Pirovolakis, UNHCR senior external relations officer, told Sky News.
She said it was proving to be a “challenge”, with psychological support being offered to women and children as they cross borders “because they have been traumatised by what is happening”.
Asked how many children are being left at the border by their mothers, she replied: “We don’t know, but the UNHCR is at the border and is looking after all unaccompanied children that are crossing and ensuring that they are protected, that the national authorities are looking to put them in protection services and that they are being cared for.
“The next step will of course be family reunion, and in these circumstances, the situation is changing all the time.”
Where are they going?
Ukrainian refugees will get the right to live and work in the EU for up to three years.
As of 4 March, more than half of them (672,000) have arrived in Poland. The EU member’s geographical and cultural closeness make it the destination of choice for people fleeing the war.
Other neighbouring countries to have taken in refugees include:
• Romania – More than 150,000
• Hungary – 144,000
• Slovakia – 90,000
• Moldova – 103,000
• Other European countries – 110,000
Ukrainians who have family in the UK will also be able to live, work and study in Britain for the same amount of time under a special visa scheme.
Poland: How refugees are getting there
The square opposite the main train station looks like a small refugee camp, with people huddling around fires for warmth and volunteers handing out food, soup and water.
Firewood is burnt to power water boilers, creating an acrid smoke that lingers over the area. Just a few metres away, children jump around in a small playground.
A woman and her elderly mother told Sky News they were waiting for a car to take them as near to the border as possible. In the freezing weather, they would walk the rest of the way.
Poland: What happens when refugees arrive?
Large numbers are arriving at the border checkpoint in Medyka.
A queue of vehicles stretching 18 miles (30km) was seen as Ukrainians waited for soldiers and police officers to question them and check their belongings.
Anya arrived in Przemysl, Poland, from Kyiv after being displaced from Donetsk, and spoke to Sky News as she was waiting to be processed.
“It was awful, now it’s rockets, big missiles – very scary, we had to hide in a shelter all the time,” she said.
Poland has opened eight reception centres for Ukrainian refugees at the Polish-Ukrainian border, where refugees can stay.
Romania: Where people are staying
Makeshift refugee camps have sprung up in places like Siret, where Romania meets Ukraine’s southwest border – about 20 miles (32km) from the city of Chernivtsi.
Arina is one of many staying in tents there with her family after spending her seventh birthday crossing into Romania.
Romanian volunteers and emergency services personnel threw her a surprise birthday, complete with a cake and gifts.
She said that the only present she wanted was to be with her “Popa” because her dad was left behind in Ukraine to fight for his country.
Almost everyone has left someone behind.
After arriving in Romania, Irena tearfully told Sky News: “When I told my mum that I will go abroad to save my life, mum was crying and telling me that maybe that she will never see me again. It was the most scary words which I heard in my life. I’m still scared, I’m still afraid that I can’t see her anymore.”
At the moment authorities are coping with the new arrivals – there is enough food, shelter and help – but the numbers are increasing.
When refugees arrive, Romanian authorities move people as quickly as they can – greeting them with food and hot drinks in the bitterly cold, snowy weather.
Once they are processed, buses take them into the local towns and villages.
Other European countries
Groups of Ukrainians have been getting into Hungary via the Beregsurany and Tiszabecs crossings, some coming from as far as Kyiv.
Moldova set up a camp of tents for refugees on the muddy grounds of a village stadium just three miles (5km) away from the Ukrainian border in Palanca.
Many refugees are arriving from the southern Ukrainian city of Odessa, which is about 25 miles (40km) away.
In Slovakia, tents were seen erected near the border with Ukraine.
Slovakian households and institutions were urged to help refugees by the government, who said they will receive €200 (£165) a month for an adult and €100 (£82) a month for a child they accommodate.
Some refugees head to other European countries after making it out of Ukraine – like Germany, where Ukrainians have been arriving in Berlin after making it to Poland.
The city’s mayor said about 20,000 are expected soon, and the city is in the process of reopening shelters that were built in 2015, when more than one million people from war-torn Syria, Iraq and Afghanistan came to Germany.
Authorities are arranging accommodation and private initiatives have sprung up, with locals offering housing, food and other support.
Others have been driving to the Ukrainian border and bringing refugees back to Germany.
Discrimination claims at borders
There have been allegations that people are facing discrimination at borders, with some black students describing segregated gates for Ukrainians and non-white people.
Tokunbo Koiki, a 40-year-old social worker, told Sky News she has been in touch with black students who were terrified.
“People said they were pushed, sent back and physically assaulted on both sides of the border in Ukraine, Romania and Poland,” she said.
Gagandeep Singh, who went to Kharkiv to study for a university course, claimed he faced discrimination at the Medyka border crossing in Poland: “There were two organised lines. One was for white people, and the other for everyone else.”
Before he entered Poland, he said that one of the Ukrainian border guards covertly told him that the policy was “one foreigner for every 15 Ukrainians”.
Ravinder Singh, chief executive of humanitarian charity Khalsa Aid, shared a video that showed a large group of Indian students being prevented from entering Poland, calling it “absolute racism”.
However the Polish ambassador to the UN, Krzysztof Szczerski, has previously said any claims of racism or religion-based discrimination at Poland’s border are “a complete lie and a terrible insult to us”.
Ms Pirovolakis said “all the national governments have assured UNHCR that all the borders will remain open to everyone”.