Regarding a matter: về việc (V/v in official letters)

Về việc means "regarding, on the matter of". Về is "about" and việc is "matter", so it's a formal "about", usually followed by an action: về việc tăng học phí (on raising tuition fees).

Its most visible job is naming the subject of an official document. Decisions, resolutions, letters and notices state their topic with về việc: Quyết định về việc thành lập Hội đồng thi (Decision on establishing the Examination Board). In the subject line of an official letter or form, it's shortened to V/v: V/v: Đề nghị cấp lại giấy phép (Re: request to reissue a permit). If you write to a Vietnamese office, put V/v and your matter at the top.

In news it's simply a formal "about" or "on": Nhiều phụ huynh có ý kiến về việc thu tiền học thêm. Many parents have spoken up about the charges for extra classes. It often follows verbs of talking and feeling: thảo luận về việc (discuss), lo ngại về việc (be concerned about).

Plain về is enough before a simple topic: nói về Huế (talk about Huế), sách về lịch sử (books about history). Về việc comes in when the topic is an action or a matter to be dealt with.

In conversation, people say về chuyện, with the everyday word for "matter": Em muốn nói với anh về chuyện tiền nhà. I'd like to talk to you about the rent.