When does eventual consistency make sense, and what are its challenges?

Everyone talks about strong consistency like it's the only way, but honestly, in a lot of todays distributed systems, it just doesn't make sense or isn't even possible. I'm really interested in actual situations where eventual consistency made a huge positive impact on a system, maybe making it faster or more available. What are some solid examples? And what were the toughest problems you ran into when building systems around eventual consistency? I'm thinking about old data, how to fix conflicts, or just helping users understand whats going on. Did you find any specific tricks or ways of doing things that really helped with those issues?