 Of working with Stewart and The-Dream, Lopez stated that: "What I love about great producers and writers is that they can take you and transport you right into this moment, but not change you. And that's what I feel like Tricky and Dream did with this record. They took that' Jenny from the Block ' side of me, which is still very much a part of who I am and will always be, and they put it right there on that track". According to Scott Shetler of PopCrush, "Run the World" contains an optimistic message and upbeat melody. Shetler particularly noted the lyric "Our love could run the world" as a good example of the optimism in the song.
