The GREATEST and LEAST functions in PostgreSQL take multiple input values and compare them to find the largest and smallest values respectively. The process starts by comparing the first two values, updating the current greatest or least value. Then it compares the current greatest or least with the next value, updating if needed. This continues until all values are compared. The final greatest and least values are returned. For example, with inputs 3, 7, and 2, GREATEST returns 7 and LEAST returns 2. If a NULL is present, the result is NULL unless handled. This visual trace shows each comparison step and how the results update.