Don't just install Varnish in front of WordPress and assume the best. WordPress by default places a cookie in the browser session and Varnish (also by default)

Don't just install Varnish in front of WordPress and assume the best. WordPress by default places a cookie in the browser session and Varnish (also by default) will vary the cache results by cookies -- in the case of PHP session IDs, it means Varnish will let each request through. Plan your caches carefully and start from the CMS side.