So low are the temperatures that some residents have been posting images of themselves throwing boiling water into the air and seeing it turn instantly into ice
Reuters
Temperatures of -37C were recorded in North Dakota. Here, trucks are seen amid icy conditions near the city of Fargo
Reuters
People in Chicago and elsewhere have been told to stay indoors if they can
Getty Images
Those who have braved the elements, such as this commuter in downtown Chicago, have wrapped up as warm as they can
The freezing temperatures in the Great Lakes region between the US and Canada have led to the formation of "cloud streets" - parallel rows of cumulus clouds streaming over the lakes' surface as seen in this US weather satellite image
AFP
Parts of the Niagara Falls in Ontario, Canada, have frozen
AFP
Also in Ontario, the city of Kingston has seen snowfall. Wind chill temperatures were forecast to be about -30C on Thursday
AFP
The cold snap is now reported to be edging eastwards. Here, the Canadian city of Montreal is seen blanketed in snow