Millennial has turned into a slur, so at this point I think the terminology needs to be superseded. The term originally meant birth between 1982-2004, with the caveat that the end of the generation might be up for discussion while the next generation was still growing. Now all of a sudden you have people calling anyone born in the 80s a "millennial", usually as a means to disparage them.
When I first heard the term, it seemed to be describing people born around 1988 or later. But I think it depends on locality, and my impression is the line is when cell phones became quasi-universal during high school.