The Story of the World is a very well known history series consisting of Volume 1--Ancient Times: Nomads to the Fall of the Roman Empire, Volume 2--The Middle Ages, Volume 3--Early Modern Times, and Volume 4--The Modern Age: From Victoria's Empire to the Fall of the USSR. The series was written by Susan Wise Bauer who also wrote The Well-Trained Mind, a classical education text that is nicely put together for homeschoolers trying to follow a classical curriculum.
I often like to read the same books as my daughter. I like to talk with her about them and also like to know if there are any messages I want to clarify. The Story of the World Volume 1 was such a case. The book was entertainingly written. She would read it as her free choice reading in first grade, read it again at home, and if I was reading to her in the evening, would select this book. After I started reading it, I realized something that bothered me greatly. The author did not seperate historical fact from illustrative stories from biblical tales. I am not religious, so this was particularly bothersome for me. I am also sure that there are religious people who do not interpret the bible literally as a historical document. Perhaps you're not Christian. Perhaps you're religious but want your child to understand history on the same footing as other children who are educated in a more secular way. In any of the these cases, if you choose to use these books, help your child to understand which are stories of a typical day, which are historical facts, and which are stories from the bible. Of course, one has to have a fairly good understanding of the bible to catch all of them.
The rest of the volumes (Volume 1--Ancient Times: Nomads to the Fall of the Roman Empire, Volume 2--The Middle Ages, Volume 3--Early Modern Times, and Volume 4--The Modern Age: From Victoria's Empire to the Fall of the USSR) are less likely to suffer from the bible-being-presented-as-fact criticism but can certainly be understood to be very worldly. By worldly, I mean that the history of the entire world is presented (what else would you expect from the title) AT THE SAME TIME. This means studying many other cultures along with Europe chronologically. I do not have a problem with studying the rise of Islam, but I don't like jumping around quite so much. I find it can interrupt the flow of the story of one area and take a while to get back into the mental frame of what was going on.