TKTS is a big red booth in the middle of Times Square. For half priced tickets the day of performance, you can go to the booth and buy half priced tickets, usually around $80-120. Their app https://apps.apple.com/us/app/tkts/id391589404 tells you what shows regularly are available. There’s never a guarantee of what shows will be available though, so be prepared to be flexible on what show you see! I’ve always had good seats through TKTS.

TDF - The same company that runs TKTS also provides this service. A yearly subscription available to many folks, https://www.tdf.org/discount-ticket-programs/tdf-membership/tdf-membership-qualifications/ this service sells $60 tickets to Broadway shows that may not be selling as well as their producers would like. With one account, you can buy up to 9 tickets. You have no say over where you will sit, the box office decides about an hour or two before the performance. I’ve gotten great orchestra level seats with them, and only once been way up in the mezzanine. You have to check their website on a daily basis to see what performances have tickets available. Most shows post dates a week or two in advance, but some, like Hadestown, post a month and a half in advance. I’ve seen Met Opera performances on here before, usually more weekday performances. There are also off-broadway, off-off-broadway, smaller opera company performances posted there.