The number of red list countries has been cut to seven, with 47 destinations - including South Africa, Mexico, Thailand and Brazil - removed.
The amber and green lists have been scrapped and rules for testing relaxed.
Red-list countries are those the government says should not be visited "except in the most extreme of circumstances".
There are now only seven destinations on the red list:
If you have been in one of these countries in the last 10 days, you cannot travel to the UK.
The only exception is if you are a UK or Irish national, or UK resident - in which case you need to:
These rules apply whether or not you have been fully vaccinated.
Rates for quarantine hotels are:
Fully vaccinated passengers travelling to the UK from any non-red list country, no longer have to take a Covid test before setting off.
This applies to people vaccinated in the UK, the EU, the US, and dozens of other recognised countries - including Brazil, Hong Kong, India, Pakistan, South Africa and Turkey.
You must be able to prove you are fully vaccinated.
Everyone under 18 - and resident in one of these countries - can also travel to the UK without taking a pre-departure test, whether or not they've been vaccinated.
All travellers - except children under five years old - still have to book and pay for a PCR test two days after arrival.
The government says you should book this test before you travel.
You also need to complete a passenger locator form.
From the end of October, fully vaccinated people coming to England will no longer have to take a PCR test two days after arrival.
Instead, they'll be able to take a cheaper and simpler lateral flow test.
Passengers will be able to send a picture of their lateral flow test to verify the result.
The Department for Transport has said NHS lateral flow devices cannot be used for travel. "Both pre-departure tests and on arrival tests must be bought from private providers," it said.
It's hoped this change will happen in time for people returning from school half-term breaks. However, no date has yet been given for its introduction.
No other UK nation has yet said it will introduce this change. Scotland and Northern Ireland have indicated that they may follow England, but Wales has said it has concerns.
If you aren't fully vaccinated - and you're 18 or over - you still have to self-isolate at home for 10 days after arrival in the UK.
You also need to
Test to Release will remain an option for unvaccinated passengers to England who want to shorten their quarantine.
The Foreign Office has removed advice to UK citizens to avoid holidays in 32 destinations, including Bangladesh, Fiji, Gambia and Malaysia.
The destinations weren't on the government's red list, but non-essential travel was not recommended because of fears about how Covid was being managed.
The change should make it easier for people to get travel insurance.
People who took part in vaccine trials such as Novavax have also been told they will now be offered two doses of another vaccine, to make it easier to travel to countries where trial vaccines are not recognised.
From November, fully vaccinated UK passengers will be able to travel to the US.
This should include people who've had the AstraZeneca jab, although the US Center for Disease Control and Prevention has yet to make a final decision.
Visitors will need to take part in testing and contact tracing.