"They" and "their" are being appropriated for the variable case: "Each applicant should bring their paperwork to the interview". This makes a lot of logical grammarians unhappy, but it solves a real problem now that "he" is no longer assumed to include "or she".
It doesn't work so well for the unknown case. Telling someone about the cool clerk at the record store is challenging when I don't know if the clerk is a he or a she. "The clerk was great. They found exactly what I was looking for." That is seriously awkward, but avoiding the pronoun every time feels unnatural. "The clerk was great and found exactly what I was looking for" works well enough in writing, but in speech, it is hard to think far enough ahead to see the upcoming pronoun problems. It was a relief to ask the clerk's name and hear "Sarah" in response; that is a traditionally female name and I could feel comfortable using "she" to refer to her.
And the issue gets more challenging from there, because he/she is a binary concept and human beings are rarely binary. Picking one pronoun or the other is easy for anyone who has a settled gender identity (which is most of us, even homosexuals and many transsexuals), but there are some people who have fluid gender identities. What pronoun refers to them? "It" certainly doesn't work.
English being what it is, lots of people are working to find a way to solve the problem, just as Ms. was invented to replace Mrs. and Miss when a woman's marital status was unknown or irrelevant; now it is a natural part of our system for addressing people. Wiktionary serves up xe as one example of a neutral pronoun:
- (nonstandard, chiefly Internet) they (singular). Gender-neutral third-person singular subject pronoun, coordinate with gendered pronouns he and she.
These nonstandard pronouns sound clunky now, but chances are very good that one of them will take hold and become common in a generation. Like gender identities, pronouns are currently in social flux and it will be interesting to see what the solution turns out to be.