The Gregorian calendar is the most widely used civil calendar in the world today. It is a reform of the Julian calendar. The calendar revision was decreed by Pope Gregory XIII, for whom it was named, on 24 February 1582. This well after the fall of Rome in 750, which many see as the end of the Roman Empire. While Roman rule of Europe ended and there were some odd problems with the Muslims from 661-1238 or so and there were some issues around the Reformation beginning in 1517, the Pope had much influence over continental Europe. In the table we see that the adoption of the reformed calendar took some time to spread.

1582 Spain, Portugal, France, Poland, Italy, Catholic Low Countries, Luxemburg, and colonies
1584 Kingdom of Bohemia
1610 Prussia
1648 Alsace
1682 Strasbourg
1700 Parts of Germany, Swiss Cantons, Protestant Low Countries, Norway, Denmark
1752 Great Britain and colonies
1753 Sweden and Finland
1873 Japan
1875 Egypt
1896 Korea
1912 China, Albania
1915 Latvia, Lithuania
1916 Bulgaria
1918 Russia, Estonia
1919 Romania, Yugoslavia
1923 Greece
1926 Turkey
2016 Saudi Arabia

The Gregorian calendar system dropped 10 days in its first year to bring the calendar back into synchronization with the seasons and, to keep it there, by adopting the following leap year rule:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 was not a leap year; the year 2000 was a leap year. 

In the Julian calendar, all years exactly divisible by 4 are leap years.

The year numbering in the reformed calendar continued the numbering system of the Julian calendar, which are numbered from the traditional Incarnation year of Jesus. Traditionally these have been called "anno Domini" (AD) but in recent times CE for "common era" has become common although some use "Christian Era". (This system had been in place since 525.)

The changes made by Gregory corrected the drift in the civil calendar which arose because the mean Julian calendar year was slightly too long, causing the vernal equinox, and consequently the date on which Easter was being celebrated, to slowly drift forward in relation to the civil calendar and the seasons.

The East-West Schism of 1054 meant that the Eastern Church remained on the Julian Calendar. Looking through the table we see that the places in the world where the Eastern Church is strong were late adopters. Much of the world uses the Gregorian Calendar more because of trade that anything to do with Easter.

Many Islamic countries us the Islamic calendar as their civil calendar although many use both the Gregorian calendar and the Islamic Calendar. 9/28/19