Heraldry probably began in England in the 12th century, possibly to help identify important individuals when their faces were obscured by armour. The College of Arms was instituted in 1483 and was empowered to make occasional visits to parts of the country, to establish whether coats of arms were being used without permission. The records of these visits, called heraldic visitations, are of great interest to genealogists as they give pedigrees of noble lines.
Three such visitations were made to Huntingdonshire:
1564: visited with Northamptonshire. The visitation has not been published: the original is at the College of Arms. It cannot be consulted directly, but the College can research it for you, for a fee.
1613: published by the Camden Society in 1848 (vol XLIII): a copy is available in the searchroom.
1684: visited with Cambridgeshire. This document was published by the Harleian Society in 1994 (New Series vol 13): a copy is available in the searchroom.
The College of Arms is still empowered to make grants of arms. If you think you have a right to a coat of arms, or if you think that someone is using arms incorrectly, you must contact the College, which is in Queen Victoria Street, London EC4V 4BT.
If you are interested in the history of arms, you could try the Heraldry Society, 44 Museum Street, London WC1A 1LH.
Huntingdonshire Archives at Huntingdon Library also has a number of books on heraldry, including Papworth's Ordinary of British Armorials (1985 reprint of 1884 edition) and Burke's General Armory (1961 reprint of 1884 edition), which you are welcome to consult.