A secret summit of superpowers is to be held in Baghdad but it is no longer secret, and a shadowy fascist group is plotting to sabotage the event. Things get complicated when enthusiastic young tourist Victoria Jones discovers a dying secret British agent Henry "Fakir" Carmichael in her hotel room, his last words - "Lucifer...Basrah...Lefarge" - propel her into investigation. "Lucifer" refers to the mastermind, Victoria's false lover Edward, who is behind the plot. "Basrah" refers to the city where certain documents were handed to certain people. "Lefarge" turns out to actually be "Defarge" and is a reference to a Charles Dickens character; it is a clue to where the aforementioned documents can be found.
An interesting comparison can be made between the romance themes of this novel and The Man In The Brown Suit, which is also primarily an adventure novel, rather than a straight whodunnit. In that book, the exciting, mysterious young man that falls into the heroine's room ends up as the romantic hero. In Baghdad, an exciting, mysterious young man also falls into the heroine's room, but he is disposed of, as is the other exciting, mysterious young man that the heroine has followed to Baghdad. A more conventional and staid archaeologist ends up as the romantic hero; Christie herself was married to archaeologist Max Mallowan by this date.