Crookshanks was Hermione Granger's pet cat. He was half-Kneazle, as evidenced by his lion-like appearance, ability to solve problems on his own without aid or teaching, and clear dislike of and ability at recognising untrustworthy persons (even if they are transfigured).
In 1993, Crookshanks was purchased from Magical Menagerie by Hermione Granger. The saleswoman from whom she had purchased him stated that he had been in the shop for a long time as "nobody wanted him". Crookshanks played an important role in the events that took place on 6 June, 1994. During the height of the Second Wizarding War, Crookshanks stayed at the Burrow. It is unknown what happened to him after the war, but it can be assumed that he was returned to Hermione.