In its chapter on numbers (and select other sections), the Chicago Manual of Style has these recommendations:
[9.33 Centuries] Particular centuries are spelled out and lowercased.
- the twenty-first century
- the eighth and ninth centuries
- from the ninth to the eleventh century
- the eighteen hundreds (the nineteenth century)
[9.35 Eras] Choice of the era designation depends on tradition,
academic discipline, or personal preference. Chicago recommends full
capitals and no periods.
[8.72 Traditional period names] Some names of periods are capitalized,
either by tradition or to avoid ambiguity.
- the Augustan Age
- the Common Era
- the Counter-Reformation
- the Dark Ages
- the Enlightenment
- the Gay Nineties
- the Gilded Age
- the Grand Siècle
- the High Middle Ages (but the early Middle Ages, the late Middle Ages)
[8.74 Historical events and programs] Names of many major historical
events and programs are conventionally capitalized. Others, more
recent or known by their generic descriptions, are usually lowercased.
If in doubt, do not capitalize.
- the Boston Tea Party
- the Cold War (but a cold war, used generically)
- the Cultural Revolution