The Royal Medals of the Royal Society of London were established by King George IV. They were further supported with certain changes to their conditions, by King William IV and Queen Victoria.

Originally they were awarded for the most important discoveries in the previous year. The qualification was changed to five years and then shortened to three years. When Victoria came to the throne in 1837 the conditions for the Royal Medals changed to operate on a three year cycle with Mathematics being one of the subjects for which a Medal could be awarded every third year.

In 1850 the conditions were changed again as follows:-

... the Royal Medals in each year should be awarded for the two most important contributions to the advancement of Natural Knowledge, published originally in Her Majesty's dominions within a period of not more than ten years and not less than one year of the date of the award, subject, of course, to Her Majesty's approval. ... in the award of the Royal Medals, one should be given in each of the two great divisions of Natural Knowledge.

Currently, three Royal Medals, known also as The Queen's Medals, are awarded annually by the Sovereign upon the recommendation of the Council, two for the most important contributions to the advancement of Natural Knowledge (one to each of the two great divisions) and the other for distinguished contributions in the applied sciences. These awards are for contributions made within the British Commonwealth.

The three medals are silver gilt.

Nobel prize winners Frederick Sanger, Max Perutz and Francis Crick (among others) have all received Royal medals during the medal's rich history.

2004 winners In 2004, Royal medals were awarded to Lord Lewis of Newnham , Sir Alec Jeffreys and Sir James Black.