What's the date today? If you're not sure, what do you do? Easy. Look on the calendar. But which calendar do you use?

The Gregorian calendar
If your year begins on January 1, and ends twelve months later on December 31, then you're using the Gregorian calendar. It was named after Pope Gregory VIII (1502-1585) who effected calendar reform in the 16th century. After initial resistance, even the Protestant countries in Europe adopted the new calendar, though the whole process took about 150 years. Today it's the most widely-used calendar in the world. Even countries with their own calendars use it for business purposes.

The Gregorian calendar is a solar calendar, as are, for example, the Baha’i, Hindu and Iranian calendars. Solar calendars have years of 365 days and are related to the changing position of the Earth in its journey around the Sun.

What is a day?
Having said that a year usually has 365 days, what is a day?

Following the ancient Egyptian custom, a day is 24 hours - the time it takes Earth to turn once on its axis. But when does the day begin? It starts at sunrise in the Hindu calendar and at sunset in the Jewish and Islamic calendars. Yet our days now start in the middle of the night, just after midnight local time. Faster travel and communications made it necessary to standardize civil time internationally.

Leap years
Unfortunately for timekeeping, Earth's orbit of the Sun isn't related to its rotation on its axis. Therefore you can't get an even number of days by dividing the year by 365. It comes out close to 365 and a quarter days. The astronomer Sosigenes (first century BCE), who advised Julius Caesar on the Julian calendar, solved this problem by adding a day every four years. Solar calendars continue to use the device of the leap year.

Leap years are a good idea, but Sosigenes's proposal wasn't a complete solution. Earth doesn't actually take 365 days plus six hours to orbit the Sun. It takes 365 days plus five hours and nearly 49 minutes. The eleven-minute difference sounds trivial unless you start adding it up over many centuries.

Problems with the Julian calendar and the seasons
In fact, by the sixteenth century, the calendar was ten days out of synch with the seasons. Thus the equinoxes and solstices were occurring ten days after the traditional calendar date. This is why the pope was concerned. Many church observances are related to the date of Easter, which itself is related to the March equinox. (Easter is the first Sunday following the first full moon on or after the equinox.)

The Gregorian calendar makes use of leap years, but not every four years. In order to stop accumulating extra days, if the end of a century is divisible by 400, there is no leap year. The year 2000 was not a leap year, but 1900, 1800 and 1700 were.

Months
Months are a relic of lunar calendars. The root of the word month is moon. Many calendars were originally based on the phases of the Moon, as this is an easily-observed and regular set of changes. It takes 29 and a half days for the Moon to go once around the Earth and return to the same position, and therefore the same phase. This is known as a lunar month or a lunation.

However, the Moon's orbit of the Earth is independent of Earth's orbit of the Sun, so the number of days in a year doesn't divide into an even number of lunar months. There are twelve lunations with eleven days left over.

The Islamic calendar is a purely lunar calendar and the calendar months alternate in length between 29 and 30 days. It's also linked to the Moon's phases. This does mean that religious observances move through the seasons as the years go on, unless the calendar is adjusted.

The Gregorian calendar has twelve months completely unrelated to Moon's phases and varying in length from 28 to 31 days. However lunisolar calendars, such as the Chinese calendar, incorporate information on both the position of the Earth in its orbit and the Moon's phases.

The week
There is one more calendar unit: the week. The ancient Greeks had ten-day weeks, but seven days was the convention in the Middle East. The Greeks and the Romans named the days of the week for planets, which themselves were named for gods. Although many European countries have day names based on the Latin ones, English has followed the Germanic tradition and named days of the week after Norse gods.

We tend to take a calendar for granted, but it is quite an exciting object when you think that behind it lie the traditions of many cultures and nearly three thousand years of history.

References:
(1) "The Calendar" https://www.rmg.co.uk/discover/explore/time/seasons-calendars
(2) "The Gregorian Calendar" https://galileo.rice.edu/chron/gregorian.html