Chinese sovereign is the ruler of a particular period in ancient China. Several titles and naming schemes have been used throughout history.
The characters Huang (皇 huáng "august (ruler)") and Di (帝 dì "divine ruler") had been used separately and never consecutively (see Three August Ones and Five Emperors). The character was reserved for mythological rulers until the first emperor of Qin (Qin Shi Huang), who created a new title Huangdi (皇帝 in pinyin: huáng dì) for himself in 221 BCE, which is commonly translated as Emperor in English. This title continued in use until the fall of the Qing dynasty in 1911.
The power of the emperor varied between emperors and dynasties, with some emperors being absolute rulers and others being figureheads with actual power lying in the hands of court factions, eunuchs, the bureaucracy or noble families. In principle, the title of emperor was transmitted from father to son via primogeniture, as endorsed by Confucianism. However, there are many exceptions to this rule. For example, because the Emperor usually had many concubines, the first born of the empress (i.e. the chief consort) is usually the heir apparent. However, Emperors could elevate another more favoured child or the child of a favourite concubine to the status of Crown Prince. Disputes over succession occurred regularly and have led to a number of civil wars. In the Qing dynasty, primogeniture was abandoned altogether, with the designated heir kept secret until after the Emperor's death.
Of the San Huang Wu Di, the three first of them were called 皇 (huang, "august (ruler)") and the five last were called 帝 (di, "divine ruler"), which can translate as either emperor, demigod human, or a superhuman. This title may have been used in the Shang and Xia dynasties, though oracle bones were found from the Shang Dynasty showing the title 王 (wáng, "king").
The king (王, wáng) was the Chinese head of state during the Zhou Dynasty. Its use during the Xia and Shang is uncertain but possible: the character has been found upon oracle bones. It was abolished under the Qin and, after that, the same term was used for (and translated as) royal princes. The title was commonly given to members of the Emperor's family and could be inherited. A poem from about 2,500 years ago said "普天之下,莫非王土.率土之賓,莫非王臣" which roughly translates as "Under the sky, nothing isn't the king's land; the people who lead the lands, no one isn't the king's subjects."
The Son of Heaven was a title of the Emperor based on the Mandate of Heaven. The Son of Heaven is a universal emperor who rules tianxia comprising "all under heaven". The title was not interpreted literally. The monarch is a mortal chosen by Heaven, not its actual descendant. The title comes from the Mandate of Heaven, created by the monarchs of the Zhou dynasty to justify deposing the Shang dynasty. They declared that Heaven had revoked the mandate from the Shang and given it to the Zhou in retaliation for their corruption and misrule. Heaven bestowed the mandate to whoever was best fit to rule. The title held the emperor responsible for the prosperity and security of his people through the threat of losing the mandate.
Unlike the Japanese emperor for example, Chinese political theory allowed for a change of dynasty as imperial families could be replaced. This is based on the concept of "Mandate of Heaven". The theory behind this was that the Chinese emperor acted as the "Son of Heaven". As the only legitimate ruler, his authority extended to "All under heaven" and had neighbors only in a geographical sense. He holds a mandate to which he had a valid claim to rule over (or to lead) everyone else in the world as long as he served the people well. If the ruler became immoral, then rebellion is justified and heaven would take away that mandate and give it to another. This single most important concept legitimized the dynastic cycle or the change of dynasties regardless of social or ethnic background. This principle made it possible for dynasties founded by non-noble families such as Han Dynasty and Ming Dynasty or non-ethnic Han dynasties such as the Mongol-led Yuan Dynasty and Manchu-led Qing Dynasty. It was moral integrity and benevolent leadership that determined the holder of the "Mandate of Heaven." Every dynasty that self-consciously adopted this administrative practice powerfully reinforced this Sinocentric concept throughout the history of imperial China. Historians noted that this was one of the key reasons why imperial China in many ways had the most efficient system of government in ancient times.
Finally, it was generally not possible for a woman to succeed to the throne and in the history of China there has only been one reigning Empress, Wu Zetian (624–705 CE) who usurped power under the Tang dynasty.
All sovereigns are denoted by a string of Chinese characters.
Examples in Standard Mandarin:
The first character(s) are the name of the dynasty or kingdom. e.g. Hàn, Táng, Wèi and Hòu Hàn.
Then follow the characters of their family and given names. e.g. Liú Bāng, Lǐ Shì Mín, Cáo Cāo, Liú Zhī Yuǎn and Liú Xiù.
In contemporary historical texts, the string including the name of dynasty and temple or posthumous names is sufficient as a clear reference to a particular sovereign.
e.g. Hàn Gāo Zǔ
Note that Wèi Wǔ Dì Cáo Cāo was never a sovereign in his own right but his son was. Thus his imperial style of Wǔ Dì was added only after his son had ascended to the throne. Such cases were common in Chinese history, i.e., the first emperor of a new dynasty often accorded posthumous imperial titles to his father or sometimes even further paternal ancestors.
All sovereigns starting from the Tang Dynasty are contemporarily referred to using the temple names. They also had posthumous names that were less used, except in traditional historical texts. The situation was reversed before Tang as posthumous names were contemporarily used.
e.g. The posthumous name of Táng Tài Zōng Lǐ Shì Mín was Wén Dì (文帝)
If sovereigns since Tang were referenced using posthumous names, they were the last ones of their sovereignties or their reigns were short and unpopular.
e.g. Táng Āi Dì Lǐ Zhù (唐哀帝 李柷), also known as Táng Zhāo Xuān Dì (唐昭宣帝), was last emperor of the Tang Dynasty reigning from 904 to 907.
Hàn Guāng Wǔ Dì is equivalent to Dōng Hàn Guāng Wǔ Dì since he was the founder of the Eastern (dōng) Han Dynasty. All dōng (east)-xī (west), nán (south)-běi (north), qián (former)-hòu (later) conventions were invented only by past or present historiographers for denoting a new era of a dynasty. They were never used during that era.
Xiang Yu styled himself, Xīchǔ Bàwáng (“西楚霸王,” lit. Hegemon-King of Western Chu).
Here is a quick guide of the most common style of reference (but not a thorough explanation) in contemporary use. Using an emperor's different titles or styles is nevertheless considered correct but not as common.