The only acceptable usage of ‘they’ used to be as a third person plural pronoun; that is, the word you use to refer to more than one person:
Marshall and Warren discovered Helicobacter pylori cause stomach ulcers. They used unconventional research methods.
There’s nothing unconventional about using ‘they’ in this way, but increasingly ‘they’ is seen referring to an individual when the person’s gender is unknown:
In the past, this would have been written:
The doctor looked at the test results. He appeared to be concerned.
It’s likely that when this usage was first established, the vast majority of doctors were male, but the usage wasn’t really about doctors; ‘he’ was the acceptable pronoun to use if the gender of the subject was unknown:
The parent looked at the test results. He appeared to be concerned.
I think we are way past pretending that ‘he’ can justifiably be used to mean he or she. He/she was considered an option for a while and does still get used, but it’s not a great solution. It’s tempting to think of ‘they’ as a modern way around this, but the Australian Government Style Manual says this “type of construction has a long history dating back more than four hundred years, but it has acquired special value recently in the context of seeking inclusive language” (p76). Expect to see it more and more. It was voted as word of the year by the American Dialect Society but its usage is by no means restricted to America; Australia’s Macquarie Dictionary describes it as a solution that is being adopted more and more these days.
In just the same way that ‘they’ can be used in a singular form, so can ‘them’. For example:
The doctor looked at the test results. It was difficult for them to interpret exactly what was going on.
In this case, ‘them’ provides a gender-neutral alternative to saying him or her.