Europe has launched a vaccination programme that it hopes will end the coronavirus pandemic and allow a return to normal life - but Germany's rollout has faced delays in some areas of the country.
The European Medicines Agency approved the Pfizer/BioNTech vaccine on 21 December and the aim is for all adults to be vaccinated by the end of 2021.
European governments are promoting the vaccine as the continent's best chance to return to normal life, with European Commission President Ursula von der Leyen saying: "Vaccination is the lasting way out of the pandemic".
German health minister Jens Spahn said on Saturday. "This vaccine is the decisive key to end this pandemic... the key to getting our lives back."
The vaccine must be stored at very low temperatures of about -70C, before being transported to distribution centres in specially designed cool boxes filled with dry ice.
Once out of ultra-low temperature storage, the vaccine must be kept at 2C to 8C to remain effective for up to five days.
But a number of areas in the German state of Bavaria had vaccine delays on Sunday, as temperature trackers showed 1,000 of the shots may not have been kept cold enough during transit.
In a statement, the Bavarian district of Lichtenfels said: "When reading the temperature loggers that were enclosed in the cool boxes, doubts arose about the compliance with the cold chain requirements."
Medical staff discovered the temperature in one vaccine transport cool box had risen to 15C, which is above the maximum of 8C stipulated by the manufacturers, said a spokesman for Lichtenfels.
He said 1,000 shots had been affected by the temperature issue and that the town and the districts of Coburg, Kronach, Kulmbach, Hof, Bayreuth and Wunsiedel in northern Bavaria were waiting to hear from BioNTech about whether the vaccine could still be used.
The EU nations have recorded at least 16 million coronavirus infections and more than 336,000 deaths, although real numbers are likely to be higher due to limited testing particularly early on in the pandemic.
Some countries have called on doctors and nurses to come back from retirement to help the vaccination effort, while some have trained people from other occupations to assist.
The 27-country bloc had planned a coordinated rollout on Sunday but Hungary, Germany and Slovakia couldn't wait and instead began vaccinating people on Saturday.
In Hungary, vaccinations started with frontline health workers at hospitals in Budapest.
In Germany, officials concentrated on care home residents, as the vaccine was prepared for distribution around the country.
Tobias Krueger, operator of a nursing home in the northeast German region of Saxony-Anhalt, said: "Every day that we wait is one day too many."
The first person to be vaccinated at that home was Edith Kwoizalla, 101, and Mr Krueger said 40 of the home's 59 residents and 10 of the 40 workers wanted the vaccine.
The first person to get the vaccine in Slovakia was an infectious diseases expert, Vladimir Krcmery.
The 60-year-old was vaccinated along with doctors at a hospital in the city of Nitra, described by health minister Marek Krajci as a "historic moment".
France received its first shipment of the vaccine on Saturday and said it would prioritise elderly people who live in groups.
Urging people to be "proud" of the French health system, President Emmanuel Macron tweeted to say the jab was not obligatory but people should "have confidence in our researchers and doctors".
He added: "We are the land of the Enlightenment and Pasteur, reason and science must guide us."
In Italy, five healthcare workers were the first to be given the vaccine, and temporary solar-powered healthcare pavilions will be built in town squares.
Italy has had the highest number of fatalities in Europe with more than 71,000 deaths from the virus.
In Spain the first doses will be given at a care home in the central city of Guadalajara.
Czech prime minister, Andrej Babis, was the first to get the vaccine in the Czech Republic on Sunday morning, ahead of the distribution of 9,750 doses across the country.
World War II veteran Emilie Repikova, 95, was second to get the jab.
In Poland, the first two people to be vaccinated on Sunday will be a nurse and a doctor at the interior ministry hospital in Warsaw, followed by medical workers in other hospitals.
The country's prime minister, Mateusz Morawiecki, said getting vaccinated was a patriotic duty.
In Bulgaria, the first person to get the jab was health minister Kostadin Angelov, who promised a campaign to promote the vaccine's benefits. Both Bulgaria and Poland have a high level of suspicion surrounding the vaccines.
Mr Angelov said he could not wait to see his father, 70, without fear of infecting him.
An 81-year-old care home resident on Sunday became the first person to receive COVID-19 vaccine in Croatia. Top officials attended as Branka Anicic received the vaccine before cameras. She says it felt great to be the first in Croatia to receive the vaccine and urged others to do the same.
Portugal will create separate cold storage units to get the vaccine to the archipelagos of Azores and Madeira.
Meanwhile, a new variant of COVID-19 that has been found in every part of the UK, has now also been detected in France and Spain.
The new strain, named VUI-202012/01, is up to 70% more transmissible.
While experts are confident the vaccine will work against this new variant, further tests will need to take place to be completely certain.