The dispute began last July, when gay rights activist Gareth Lee placed an order with Ashers for a cake bearing the slogan 'Support gay marriage'.
It was requested to mark International Day Against Homophobia and Transphobia, but the bakery turned down the order and returned Mr Lee's deposit.
Family-run Ashers said it conflicts with their Christian beliefs about marriage being between a man and a woman.
That decision prompted Mr Lee to speak to the Equality Commission, which threatened Ashers with legal action over discrimination claims, before pressing ahead with the case in November.
He will be claiming "modest damages" for the upset and inconvenience caused.
The DUP reacted by introducing a Private Member's Bill - the so-called 'conscience clause' - that would allow businesses to refuse services if they clash with their religious beliefs.
If passed, companies with a moral objection could turn down customers without the fear of breaching equality legislation.
A public consultation on the Bill closed at the end of February, and Sinn Fein has claimed it gathered enough support across the Assembly for a petition of concern, which would block the clause.
The 'gay cake row' has made national headlines, was raised at Prime Minister's Questions and was a talking point on radio shows as far afield as Australia. Elsewhere, a US-led petition against the conscience clause has attracted more than 200,000 signatures from around the world.
Actor and presenter Stephen Fry has also been a high-profile objector to the clause.
Fry, who married his partner earlier this year, described the Bill as "sick".
He urged his Twitter followers to sign a petition against "the religious Right twisting truth to present themselves as victims".
The dispute has also had a ripple effect in the Republic of Ireland, where the Catholic Archbishop of Dublin called on the government to implement a similar provision, ahead of the referendum on same-sex marriage.
Archbishop Diarmuid Martin's proposal was rejected by a sex rights group, which claims it is "legalising discrimination".
The Ashers company is named after one of the 12 tribes of Israel in the Old Testament who were reputed to be gifted bakers.