Bud and Lou, the faithful pet hyenas to Harley and Joker, made their first appearance in the episode "The Man Who Killed Batman." One might guess that the Joker has pet hyenas because they are known for laughing. In their first appearance, they were shown chowing down on a henchman that spoke up to the Joker. Their names were never revealed until the episode "Joker's Millions," when Joker makes a comment about how they will soon be rich. The two are named after Bud Abbot and Lou Costello. Since their first appearance, Harley has kept Bud and Lou with her, mostly when she is away from the Joker. She probably thinks of them as her children since she knows the chances of her having the Joker's are very slim.
The picture at the top is drawn by Harleen and was used with permission. To see more of her Harley art and other work, visit KC's Gallery.