The extent of the damage in Jamaica will not begin to become clear until daybreak - but Holness warns of damage to homes and hospitals. BBC reported.
The mayor of Montego Bay tells the BBC the first thing they will do is "check if everybody is alive" - our reporter in Kingston says he's unable to reach people to see how they are
After hitting Cuba, the hurricane will move north-east towards the Bahamas and Bermuda
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Hurricane Melissa has made landfall in Cuba. The category three hurricane is hitting the south east coast of the country with sustained winds of 120mph.
In Jamaica, which was battered by the then category 5 hurricane yesterday, locals are waiting for daylight to assess the damage.
After hitting Cuba, the hurricane is expected to weaken as it moves north-east towards the Bahamas and Bermuda.
And in Haiti, to the east of Cuba, people have been seeking shelter in buildings such as schools. It is not thought that the eye of the hurricane will pass over Haiti.
Here's a look at the path of the hurricane, which is expected to travel away from the Caribbean islands later this evening.