They can break your arm and are all owned by the Queen, so it is often said.
But at least one of these two claims about swans has some truth to it... as a rare Tudor manuscript confirms.
The document, which is due to go up for auction next month, was written in the 16th century as a guide to swan-keeping in Norfolk and Suffolk.
A favourite delicacy for the banqueting table, the mute swan has been deemed a royal bird from the Middle Ages.
The manuscript describes how all swans flying free on open and common waters were deemed the property of the crown, and it outlined what rules landowners should observe in their dealings with the birds.
Only the monarch could grant the privilege of owning a 'game' of swans, to individuals or institutions.
All such birds had to be marked and pinioned to help with any dispute over ownership, or for swan upping - the annual overseeing of the marking of the new cygnets.
A Swan-Master was appointed both to care for the royal swans and to oversee and regulate swan-keeping throughout England.
He was assisted by deputies with responsibility for a specific and manageable region.
The two-volume manuscript, which has been included in a sale at auctioneers Sworders, in Stansted Mountfitchet, Essex, was used from the 16th to the 19th century by landowners in Norfolk and Suffolk.
It references the ‘Hundred of Wisbech’.
The first volume, dated 1566, contains more than 600 marks - identifying notches made on the birds' beaks - followed by 19 pages of manuscript notes concerning the ‘Laws and Ordinances regarding swan’.
The names start with the Dukes of Norfolk and Suffolk, on to the Bishop of Ely and the Dean of York and finish with wealthy landowners.
The second volume is dated 1834 and includes notes on swan marks followed by 84 pages of swan marks and an index of owners.
It will go under the hammer in Sworders' August 23 sale of books and maps, and has a guide price of £8,000 to £16,000.
So does the Queen still own all the swans?
These days, according to the Royal Family's website, the Queen retains the right to claim ownership of any unmarked mute swan swimming in open waters.
But this right is mainly exercised only on certain stretches of the River Thames.
Swan upping still takes place once a year on that river, with cygnets weighed and measured and checked for injuries.
The young cygnets are ringed with individual identification numbers that denote their ownership if they belong to the Vintners or the Dyers livery companies.
The event has changed from a mostly ceremonial event to one of wildlife conservation.
... and can they break you arm?
Male swans can be very aggressive and fierce in defence of their nests, especially during nesting season from April to June. But no, they can't break your arm.
As John Hutson, of the Abbotsbury Swannery in Dorset, told the BBC: "It’s a myth that they will break your leg or arm with their wings. They are not that strong and it’s mostly show and bluster."
Norwich's Swan Pit
Norwich boasts a very rare example of a late 18th century swan pit, where swans were kept to be fattened up.
Visible from the Riverside Walk, the pit, with attached sluices, linking to the River Wensum, is in the grounds of the Great Hospital.
It is a large rectangular pool with brick sides and paved ramps at both eastern corners.
Sluice gates ensured the pit was filled with water at high tide and was not allowed to empty at low tide.
The Grade II-listed pit was used for the breeding of local swans for the Master of the Great Hospital, Norwich, who since medieval times had the right to cull swans and provide them for feasts.
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