I had a phone interview scheduled, but the interviewer didn't end up calling me, even after 30 minutes.
What should I do afterwards?
I had a similar situation recently and I sent this back via email after about 30 minutes of waiting for a phone call:
It looks like this time did not end up working. Is there another time which would work this week?
You don't want to be accusational. You have no idea why the interviewer didn't call. Maybe something urgent came up at work (you aren't an urgent priority generally). Maybe they had a family emergency. Maybe they were sick. Lots of possibilities. Maybe they just forgot to add it to their calendar. Maybe their phone was dead.
Anyways, whatever you do, don't assume ill intent.
What do you do afterwards? Is an email-reminder a good way? Or just move on?
I definitely wouldn't just act as if nothing happened. Keep in mind while the interview for you is a big deal, for the interviewer it's just 30 min in a day of other far more pressing priorities.
Sending a simple followup email without making accusations is absolutely acceptable. Be careful though - a "reminder" isn't what you necessarily are going for.
Just a note, this is a great time to make sure you determine an alternate or backup plan when having a phone interview prior to not connecting.
Wait an hour or two and, if you haven't heard anything from them, give them a call yourself and ask what's up. Mistakes happen. People lose track of time, something comes up, meetings go long, or maybe their calendar borked and they forgot about you. Definitely don't assume that just because you didn't get the phone call you were expecting that you should just move on.
If you can't get a hold of the specific person who was supposed to call you, try to get a hold of someone that can investigate for you or verify information. Not everyone has a receptionist that keeps track of all their appointments, or a person they can just tell "hey, cancel all my appointments for me." Maybe they had to go pick up their kid from school because they were sick and just completely spaced off the phone interview they were supposed to conduct. There's so many possibilities.