What distinguishes Chinese astrology from the Western tradition is that it is not a specialism at all. Yin and yang, the five agents and the stem-branch cycle are the shared framework of calendar, medicine, divination, geomancy and statecraft, and a Bazi reading uses exactly the same apparatus as a diagnosis in traditional Chinese medicine or a siting in feng shui.
The system took its recognisable form under the Han dynasty, when correlative cosmology was systematised into state orthodoxy: five agents matched to directions, seasons, colours, organs, flavours, tones and dynasties, so that the whole of experience could be laid out on a single grid. The sexagenary cycle is older, appearing in Shang oracle bone inscriptions for counting days. Bazi as a personal method is usually credited to Xu Ziping in the tenth century, which is why the method is often called the Ziping system; earlier personal astrology in China worked from the year pillar alone.
The imperial state maintained an Astronomical Bureau whose work was simultaneously calendrical, astronomical and ominous, and access to some of this material was legally restricted, since prediction about the dynasty was a political act.
Practitioners today read a chart for temperament, career suitability, health tendencies, compatibility and the timing of favourable and unfavourable periods, and the compatibility application is the one most visible in popular culture across East Asia, to the point that birth rates measurably dip in Dragon and Tiger years in several countries, an effect demographers have documented. That is a real social consequence of the belief, and it is a different thing from evidence for the system.
The tradition remains woven into ordinary life in China, Taiwan, Hong Kong, Vietnam, Korea and Japan through festivals and the naming of years, and professional Bazi consultation is a substantial commercial practice.