Bud and Lou were a pair of hyenas owned by the Joker and Harley Quinn. Harley is the one responsible for their care, and she affectionately refers to them as the "babies".
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Bud and Lou are named after comedy duo Bud Abbot and Lou Costello. The basic idea of Joker having hyenas as pets was later carried over to other TV series as Krypto the Superdog, The Batman, and the videogame Batman: Arkham City.
According to the DVD commentary for Batman Beyond: Return of the Joker, the addition of the character Woof, a gene-spliced hybrid of man and hyena, as a member of the Jokerz gang was a direct homage to Bud and Lou.