The Gregorian calendar is used throughout most of the modern world. Invented in 1582, the system adopted a leap year cycle different than the one employed by the Julian calendar. The new calendar was considered an improvement on the earlier Julian model. In the Gregorian calendar, four years make up a cycle, with an extra or “leap” day added to the fourth year to keep the dates and months synchronized with the solar cycle.
Although the Gregorian calendar was named for Pope Gregory XIII, who sanctioned its use, it was created by an Italian doctor named Aloysius Lilius. The Julian calendar, in use for centuries, did not have a system in place to make the dates of the equinoxes, and consequently the Catholic holidays associated with them, fall on the same day. In addition to dropping ten days from the Julian system, the Gregorian calendar introduced different rules to the leap year system to establish consistent dates in relation to the equinox. This new approach allowed Christmas, for example, to fall on December 25th every year.
In the new system, there were twelve monthly divides of similar, although unequal lengths. February, the second month, was the only month to contain 28 days, so the added day in leap years was solidified as 29 February. Leap years exist once every four years, and only occur in years that are divisible by four. There is an exception to the divisible-by-four-rule, and that is if the year ends in -00. Even though years ending in -00 are divisible by four, it is not a leap year. However, there is one more exception to the exception. Years ending in -00 that can be divided by 400 are in fact leap years.
The Gregorian calendar was decreed valid by Pope Gregory XIII on 24 February 1582, but was not accepted by any European nations until October of that year. The first countries to begin mandating the use of the calendar were Spain, Portugal, Italy, and the Polish-Lithuanian Commonwealth. France and Holland quickly followed, both adopting the new method before the end of 1582.
Non-Catholic countries understandably had reservations about accepting a calendar specifically aimed at furthering the goals of the Roman church. Europe was heavily involved in the Protestant reformation when the calendar was proposed, and anti-Catholic sentiment long postponed the unification of Europe under a common calendar. Eventually, the benefits of a common date system became impossible to dismiss, and while the calendar had been created at the whim of the Catholic Pope, its scientific basis made a considerable amount of sense.
It took several centuries, but by 1929 most countries in the world had begun using the Gregorian calendar. China, the last nation to adopt the system, technically accepted it beginning in 1912, but civil unrest left the calendar question undetermined until the unification of the country in 1929. Other countries, such as Japan, accepted the use of the calendar for dealings with the western world, but still maintained local systems in place for centuries.
Typically, when talking about dates prior to the 1582 institution of the calendar, scholars continue to use the Gregorian count retroactively. Occasionally, you may come across dual dating, which uses both Julian and Gregorian years. This most often refers to the interim time when the Gregorian calendar may not yet have been accepted, but was already in wide use.