Image copyright PA Image caption In 2002 this dog was the first to travel to the UK using a pet passport

When the UK was a European Union (EU) member, you could take your pet dog or cat from the UK to the EU and back again without them having to go into quarantine, provided that certain conditions - such as having a pet passport or getting them microchipped - were met.

That will continue to be the case for the rest of 2020 while the UK is in a transition period with the EU. During this time, almost everything is staying the same.

From 1 January 2021, you will no longer be able to use pet passports. Instead you will need to follow a different process.

The government website says you should contact your vet at least four months before travelling, to get the latest advice.

Pet passports are issued by EU countries and a short list of other countries such as Greenland, Iceland and Switzerland.

The UK could be added to this list, but agreements would be needed to make that happen - it would not be automatic.

If it did, the UK would be classed as a Part 1 listed country or a Part 2 listed country.

Part 1 listed country

Being a Part 1 listed country is very similar to the current situation, except that you would have to apply for a UK pet passport instead of an EU one.

Your pet needs to be microchipped and vaccinated against rabies at least 21 days before travel.

Dogs may also need to be treated for tapeworm.

Part 2 listed country

If the UK becomes a Part 2 listed country then on top of the above you will need to visit an official vet no more than 10 days before you travel to get an animal health certificate (AHC) confirming that your pet is microchipped and vaccinated against rabies.

You will need to get a new AHC each time you travel with your pet.

Unlisted country

If the UK ends up being an unlisted country then, in addition to the requirements above, you will need to have a blood sample taken from your pet at least 30 days after its last rabies vaccination, which will then be sent to an EU-approved laboratory.

You will have to wait at least three months from the date the successful blood sample was taken before you can travel.

The blood test results will go on your pet's AHC.

Image copyright Getty Images

UK citizens living in the EU

If you live in the EU and have a pet passport issued by an EU member state, you will be able to use it to bring your pet to the UK after 2020, even if the UK becomes an unlisted country.

You will be able to return to the EU with the EU-issued pet passport as well, as long as your pet has had a successful rabies antibody blood test, taken at least 30 days after the date of rabies vaccination.

If the UK ends up as an unlisted country and the blood sample is taken in the UK, you will have to wait 3 months from the date of the test before you travel back to the EU.

What do you want BBC Reality Check to investigate? Get in touch

Read more from Reality Check

Follow us on Twitter