Optimizing Cache Invalidation in Large-Scale CDNs, A Practical Debate

That CDN design article really got my brain working on cache invalidation. I mean, with a CDN that's got millions of files and users all over the world, how do you even update stuff fast while still keeping the cache working well? I'm trying to figure out the real world give and take between pushing out invalidations (like using a publish, subscribe system) and just letting caches expire naturally (you know, with TTLs and checking stuff when someone asks for it). Does it change a lot for different businesses, like if you're doing live video versus just serving up pictures? And what big problems have you hit with invalidation on a massive scale, and how did you fix them?