Their first engagement was at Hillsborough Castle.
The Queen held a private audience with First Minister Peter Robinson and deputy first minister Martin McGuinness.
Prince Philip met about 75 recipients of the Duke of Edinburgh gold awards.
After arriving at Belfast City Airport, the Royal Couple were greeted by Secretary of State Theresa Villiers and the Lord Lieutenant for Belfast Dame Mary Peters.
Tomorrow, Tuesday, they will visit the Game of Thrones set in the Titanic Quarter in east Belfast and also take a tour of Crumlin Road gaol in Belfast.
Afterwards, the Queen and Duke of Edinburgy will also be a visit to St George’s market on Tuesday, which will have stalls from the Friday, Saturday and Sunday markets.
The market will be open to the public.
Security is expected to be tight on Tuesday in and around Belfast as the couple make their way from the east of the city into the town centre.