When did BCE end and CE begin?

BCE (Before Common Era) and CE (Common Era) are basically the same as BC (Before Christ) and AD (Anno Domini).

The "Common Era" (CE/BCE) notation has been adopted as an alternative of the BC/AD by those who wish to be neutral or sensitive to non-Christians.

So, BCE ended 2011 years ago and CE began at the same time.

BCE and CE are the politically correct terms for BC and AD.

There was no 'year zero'.

The last day of the last year of BC was 31 December 1 BC.

It was followed by the first day of the first year of AD: 01 January 1 AD.

Do you mean when did people start to say "common era" and "before common era" rather than "anno domini" and "before Christ?"

The earliest use of the expression was in nineteenth-century Jewish writers, who were naturally reluctant to use "year of the lord" (the meaning of Anno Domini) but wanted to use dates that would be comprehensible to non-Jewish readers. It very gradually gained ground over the years but the real pendulum swing toward using came in the 1980s when it became standard usage for many publishers and textbooks.