Here's a summary from the BBC outlining the cases:
Nadia Eweida, a Pentecostal Christian from Twickenham, south-west London, who was sent home by her employer British Airways in 2006 after refusing to remove a necklace with a cross
Devon-based nurse Shirley Chaplin, who was moved to a desk job by Royal Devon and Exeter NHS Trust Hospital for similar reasons
Gary McFarlane, a Bristol relationship counsellor, who was sacked by Relate after saying on a training course he might have had a conscientious objection to giving sex therapy advice to gay couples
Registrar Lilian Ladele, who was disciplined after she refused to conduct same-sex civil partnership ceremonies in north London
Each individual had made a separate application to the court, but the cases are being heard together.