More can be written, but for overviews of Greece and Rome, you might like to start with "BC / AD - what did they use at the time?" by [deleted], /u/azdac7, and /u/mmilosh. For more detail on Greek systems, you can see "How did the ancient greeks write the date? And how did they refer to past dates?" by [deleted]. Both of these are out of the FAQ page "Calendars and timekeeping".
This is not to discourage discussion. More questions, data and debate are welcome.