Monsters: Dark Continent takes place 10 years after Monsters. The "infected zones" in the first film are now worldwide. Dark Continent focuses on the Army's efforts to combat the alien monsters in the Middle East. This war weary alien invasion film looks larger that the first and I'm really looking forward to watching it.
Because of the time gap and the story's focus, watching Monsters is not a requirement for being able to watch Dark Continent. But I do highly recommend watching the first film because it's the film that got Gareth Edwards the directing gig for Godzilla.
Monsters: Dark Continent fights back at a time to be determined, because it currently has no US release date.