It was the voyage which paved the way for colonisation of the New World, as just over 100 pilgrims and 30 crew set sail for the East coast of America in 1620 from Plymouth's Barbican.
More than 30 million people can trace their ancestry to the crew and passengers of the Mayflower.
16 September 2020 marked 400 years since the start of the voyage of the Mayflower.
So who were the Pilgrims and what about the indigenous people who already lived in America and whose lives would be so affected by the new arrivals?
The Pilgrim Fathers, as they became known, originated as a group of Puritans from Nottinghamshire and Lincolnshire. These were Christians who were unhappy with the Church of England and wanted worship, and the way the church was run, to be more like that described in the Bible.
Known as Separatists, they were quite extreme and refused to attend services, for which they were fined.
They fled England and settled in the Netherlands but many were unhappy and saw the chance for freedom and a new life in the New World or America.
They came back to England with a view to travelling there and the plans for the Mayflower became a reality.
The Pilgrims were not the only ones on board. After delays and disagreements they ended up making up only 37 of the 102 passengers.
The others were on the ship for a range of reasons – looking for a better future for them and their families, opportunities to own land and to make money, the attraction of adventure and for a few, an escape from persecution or even prosecution.
There were also around 30 members of the crew.
The sailing of the Mayflower
The colonists had planned to travel from England in two ships, the Mayflower and the Speedwell. Unfortunately the Speedwell was unseaworthy and had to be abandoned.
The Mayflower set sail from Plymouth on 16 September 1620 and took 66 days to cross the Atlantic.
The ship was beset by winter storms and sometimes it was so bad that the crew could not use the sails and the ship simply drifted. A passenger was even washed overboard but fortunately was rescued. One woman, Elizabeth Hopkins, gave birth to a baby boy, aptly named Oceanus.
Plymouth historian Chris Robinson says the weather was horrendous for the crossing.
The Mayflower finally dropped anchor off Cape Cod on 11 November 1620. Soon afterwards, Susannah White gave birth to a son, the first English child born in the colony. He was named Peregrine, from the Latin for pilgrim.
A whole new world
The pilgrims had permission from the King of England to settle on land near the mouth of the Hudson River - present-day New York - but instead chose to stay where they had landed in New England.
They signed the 'Mayflower Compact' so that order could be kept and the colonists would work together. It was an agreement that is said to have influenced the Declaration of Independence.
Isabelle Richards works at the Pilgrims gallery at the Bassetlaw Museum in Nottinghamshire where they dress up in period costume to enhance the experience. She says that although there had been visitors from Europe before, these wanted to settle rather than plunder.
The pilgrims started to build their new homes at what now is Plymouth Bay, while still living on the ship. Arriving in November, they were unprepared for the harsh weather - only half of the original pilgrims survived the first winter at Plymouth.
Sue Allen, Pilgrim historian, tells the story of Francis Eaton from Bristol, one of the survivors, who encountered terrible hardships.
Without the help of local indigenous people, the Wampanoag, to teach them how to gather food and other survival skills, the colonists might all have died.
The following winter, the colonists celebrated their first harvest alongside the Wampanoag, which became the first Thanksgiving, which is celebrated every November in the United States.
The Wampanoag are native Americans and have lived in Rhode Island and Massachusetts for more than 12,000 years - long before the pilgrims arrived.
Their name means People of the First Light.
In 1600s they had around 40,000 people across 67 villages but were struck by disease - which was almost certainly of European origin.
The Great Dying, as it was called, killed tens of thousands of them, weakening the Wampanoag nation politically and economically. One of the villages wiped out was Patuxet, which was taken over by the pilgrims to become Plymouth Colony.
In 1621, an English-speaking Wampanoag man called Tisquanto taught the pilgrims how to plant corn, fish and gather nuts and berries.
In March 1621, the pilgrims made a peace treaty with Massasoit, one of the tribes' leaders. In November the famous first Thanksgiving took place - although it was more a case of a harvest feast that the Wampanoag turned up at, than the turkey affair it is today.
The peace treaty lasted for 50 years until there was a rebellion against the colonists' control, known as King Philip's War. Around 40% of the surviving tribe were killed and many were sold into slavery.
The tribes largely disappeared over the years but there are still 4,000-5,000 of the Wampanoag alive today, mainly living near a reservation at Martha's Vineyard.
In an interview with Mayflower 400, Paula Peters from the Wampanoag Nation Advisory Board says it is ironic that a group of people who were seeking the space to worship in freedom should want to control those who were already there.
Nowadays many Native Americans do not celebrate the arrival of the pilgrims and other European settlers to America.
To them, Thanksgiving is a reminder of the genocide of millions of their people, the theft of their lands, and the destruction of their cultures.
The Mayflower Legacy
More than 30 million people can trace their ancestry to the Mayflower. They include celebrities and US presidents.
Actors Clint Eastwood, Bing Crosby, Katharine Hepburn, Humphrey Bogart and Richard Gere were all descended from those aboard, along with presidents Zachary Taylor, Franklin D Roosevelt and George Bush Sr and George W Bush.
Here is genealogist Brenton Simons, himself a Mayflower descendant:
One major legacy of The Mayflower is its role in pioneering democracy. Adrian Vinken, the Chair of Mayflower 400 says, "America as a democracy was seeded by the voyage of the Mayflower and the people who were on it and why they made that voyage.
"It became, via the Declaration of Independence the most powerful democracy in the world and a model for other democracies."