Making an opening statement, Lord Justice Goldring said the tragedy was "the worst ever disaster at a British sports stadium".
The disaster unfolded on 15 April 1989 during Liverpool's FA Cup semi-final against Nottingham Forest.
The hearing could last a year.
Earlier, the inquest listened for six minutes while the names of the 96 victims were read out by Christina Lambert, counsel to the inquests.
Lord Justice Goldring said: "The disaster is seared into the memories of the very many people affected by it, most notably of course the families of the 96 people who died."
He told the jury panel of seven women and four men that the findings in the original inquests were quashed in December 2012.
Angus Crawford at the "unique" court being used for the Hillsborough inquestsThe verdicts of accidental death were quashed after the Hillsborough Independent Panel delivered its final report on the disaster earlier that year.
Over the course of the inquests, jurors are expected to hear evidence on themes including stadium safety, emergency planning, crowd management and the response of the emergency services.
The inquests are being held in a purpose-built courtroom, the biggest in England and Wales, in an office building in Birchwood Park, in Warrington.