how do you handle database migrations without taking your site down for updates?

so, we're trying to break apart our services, and we're getting closer to being able to deploy without any downtime. we have some good ideas for code updates, but changing database schemas is still a big problem. if a migration goes wrong, we might have to take the system down to fix it. and just doing migrations one way, with a delay before we switch over, feels pretty complicated. what have you guys actually done to make zero-downtime database migrations work? any tools or ways of doing things that really helped