Periods in a calendar (such as years and months) are usually, though not necessarily, synchronised with the cycle of the sun or the moon. The most common type of pre-modern calendar was the lunisolar calendar, a lunar calendar that occasionally adds one intercalary month to remain synchronised with the solar year over the long term.
A large number of Ancient Near East calendar systems based on the Babylonian calendar date from the Iron Age, among them the calendar system of the Persian Empire, which in turn gave rise to the Zoroastrian calendar and the Hebrew calendar.
The first calendar reform of the early modern era was the Gregorian calendar, introduced in 1582 based on the observation of a long-term shift between the Julian calendar and the solar year.
There have been a number of modern proposals for reform of the calendar, such as the World Calendar, International Fixed Calendar, Holocene calendar, and, recently, the Hanke-Henry Permanent Calendar. Such ideas are mooted from time to time but have failed to gain traction because of the loss of continuity, massive upheaval in implementation, and religious objections.
Solar calendars assign a date to each solar day. A day may consist of the period between sunrise and sunset, with a following period of night, or it may be a period between successive events such as two sunsets. The length of the interval between two such successive events may be allowed to vary slightly during the year, or it may be averaged into a mean solar day. Other types of calendar may also use a solar day.
An arithmetic calendar is one that is based on a strict set of rules; an example is the current Jewish calendar. Such a calendar is also referred to as a rule-based calendar. The advantage of such a calendar is the ease of calculating when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore, even if the calendar is very accurate, its accuracy diminishes slowly over time, owing to changes in Earth's rotation. This limits the lifetime of an accurate arithmetic calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar.