Varnish supports the ESI (Edge-Side Includes) standard, which allows it to cache fragments of a page, and for the cache server to build them again. It also allows you to completely bypass the cache for certain fragments. This is also supported by a number of CDNs (Fastly, Akamai). I've used the ESI technique several times and have been able to achieve a >98% cache hit rate on Fastly for a site with dynamic per-user content. Even the cache misses are only responsible for rendering a small component of the page