when should you start thinking about client-side caching

We all know about server-side caching, like using Redis or Memcached, and CDNs for static stuff. But what about caching data right in the browser or a mobile app? I'm wondering when it actually makes more sense to do client-side caching instead of it just causing headaches. What's your take on it? Any go-to methods or things you've learned along the way that really help?