Answer:
The example par excellence is Trump's presidential election which took by surprise the national and state election polling, which had had forecast Hillary Clinton as defeating Donald Trump.
One fact that could explain the inaccuracy of many pre-election data was the wide variety of methodologies being tested and streamed via the media.
Another fact that could affect polls in 2016 was that some demographic voting groups were hard for pollsters to reach.
Also, to hire a well-known polling firm is not necessarily hiring the most accurate polling service.
You should know how firms conduct their polls (online, telephone or robopolls, etc.). Telephone polls have legal restrictions for automated calls to cellphones under several circumstances. This states a reach challenge for telephone and online polls for those key demographic groups which finally decides in ballot boxes.
Polls calculation of bias was commonly estimated without taking into account an average error in the measures. Nowadays, a bias calculation should correlate several surveys, poll firms, and statistical techniques to calculate an average error and an average statistical bias.
Political polling has become more complex and now its complexity determines its value.
It's necessary to remember that political polling main use in a democracy is not to determine who is going to win an election or popularity but to build an equal voice about the public's needs, wants and claims.
Retrieved information from Pew Research Center and The New York Times.