The system used for scoring in Olympic gymnastics is called the Code of Points. This detailed scoring system evaluates gymnasts based on the difficulty and execution of their routines. Each routine consists of various elements, and judges assess performance on a scale, deducting points for errors. The final score is determined by summing both the difficulty score (representing the complexity of the performed skills) and the execution score (measuring overall performance quality). This intricate system ensures fair competition and accurate representation of an athlete's capabilities.