How Polls Got Brexit "Wrong"

Continuing the discussion of how polls do (and sometimes don't) tell us what to expect in upcoming elections--let's take a concrete example from the recent past, shall we? The Brexit referendum was, by and large, expected to shake out for "remain", but when the votes were counted, "leave" came out ahead. Everyone was shocked (SHOCKED!) but maybe the polls weren't as wrong as the pundits like to claim.

Relevant links:
http://www.slate.com/articles/news_and_politics/moneybox/2016/07/why_political_betting_markets_are_failing.html
http://andrewgelman.com/2016/06/24/brexit-polling-what-went-wrong/