Modern is a constructed format that allows expansion sets and core sets from Eighth Edition forward, save for the Modern ban list. The modern format thus encompasses all cards that have been printed in a core or expansion set using the modern card frame (plus some others from Time Spiral).
The format was introduced as a non-sanctioned Magic Online format in May, 19, 2011. And subsequently officially codified on August 12, 2011, when the format of Pro Tour Philadelphia was changed from Extended to Modern.     
Constructed decks must contain a minimum of sixty cards. There is no maximum deck size; however, you must be able to shuffle your deck with no assistance. Like other constructed formats, a sideboard of at most of fifteen cards can be used.
With the exception of basic land cards, a player's combined deck and sideboard may not contain more than four of any individual card, counted by its English card title equivalent. All cards named Plains, Island, Swamp, Mountain, and Forest are basic, as are their snow-covered counterparts — Snow-Covered Plains, Snow-Covered Island, Snow-Covered Swamp, Snow-Covered Mountain, and Snow-Covered Forest. 
As of September 26th, 2014, cards from the following sets are permitted in Modern tournaments :
† This includes timeshifted cards. Even it is printed as older frame
- See also: Timeline of DCI bans and restrictions.
As of January 23rd, 2015, the following cards are banned in Modern tournaments:
- Modern Death Cloud Rock deck
- Modern Delver deck
- Modern Infect Combo deck
- Modern Living End deck
- Modern Melira deck
- Modern Mystical Teachings deck
- Modern Pyromancer deck
- Modern Zoo deck
- Pro Tour Philadelphia Format Change
- Tom LaPille. (May 27, 2011.) "A Modern Proposal", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Tom LaPille. (August 12, 2011.) "Welcome to the Modern World", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Tom LaPille. (November 04, 2011.) "The Modern Future", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Sam Stoddard. (June 21, 2013.) "Developing Modern", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Sam Stoddard. (February 21, 2014.) "Modern Living", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Modern Format Deck Construction, MTG.com