how do you deal with eventual consistency when you're using microservices

So, I'm building this system with a bunch of microservices that need to talk to each other. We're trying to go with eventual consistency so things aren't so tightly linked, and I'm wondering how you all do it. Are you mostly using message queues, like Kafka or RabbitMQ, to get changes out there? Or maybe you prefer a choreography style with events? What are the biggest headaches you've hit when setting up and fixing these eventually consistent processes?