Many people use "BCE", or Before Common Era, but that's somewhat like putting lipstick on a pig: The baseline year is still the (probably wrong) year of Christ's birth. The current dating system came into widespread use in the Middle Ages, when the Church was a primary keeper of records. It replaced earlier systems that used reginal years or local events, and granted consistency between countries. When combined with the Gregorian system, it is accurate and doesn't require astronomical observations or large corrections.

There have been some efforts to replace it, but the current system is deeply entrenched in society, not only in history books but in software and hardware. Replacing it would be costly and confusing for no real purpose (which doesn't stop people from trying). I think it would take some great worldwide event that everyone could agree heralded a new epoch.

The short answer is that it isn't normally used anymore, having been mostly replaced by CE/BCE by the majority of academics, including History. However it still features heavily in texts published before the 2000s, so it's still a common feature when researching.

Historically, societies were much more secular, with most education centres, such as the original universities in the UK, and much of Europe, being ran by and set up by religious organisations. The use of AD and BC in scientific debate dates from this time, with atheist /agnostic scientists still using them, as that is both what they were taught with and what the international scientific community of the time would use.

The expression "Vulgaris Aerae" was in use from 1615, the English form "Vulgar Era" in 1635, and "Common Era " from around 1718. They are used contextually and interchangeably with the term "Christian Era" or AD by monks and other Christians throughout this time. They were common sayings among priests, scientists and laymen alike and featured as synonyms in many encyclopedias between the 17th century till the early 19th.

(it was called the vulgar era to distinguish from the normal historical groupings based on the ruling monarchs, with different "Regal Eras", such as the Georgians, Edwardians, Normans etc in the UK)

In the 19th century, Jewish Academics started to use "Common Era" and the "CE" abbreviation to denote history in a way that did not reference Christ. Over time this noon secular abbreviation has become more common, especially since the 1980s.

Now the terms CE (common era) and BCE (before common era) have actually mostly replaced AD and BC, as they are more accepting of other religions. It is quite rare that a modern academic text will use AD and BC, with most subjects using CE and BCE as far as I am aware.

Other abbreviations used through history are the Pseudo - Latin "Era Vulgaris" (e.v/EV) populised by Aleister Crowly, and VE, for Vulgar Era, which was used by some Jewish Academics before the consensus was to use "Common Era". This is often found on historical Jewish Headstones. Both are rare to find, even in a historical text from the relevant eras.