Let G be a finite group, let A be a prime block of G having an abelian defect group P, let N be the normaliser in G of P, and let B be the Brauer correspondent of A. Then the abelian defect group conjecture says that the bounded derived categories of the module categories of A and B equivalent as triangulated categories. Although this conjecture is in the focus of intensive studies since two decades now, it has only been verified for certain cases and a general proof seems to be out of sight. In this talk, we briefly introduce the notions to state the abelian defect group conjecture, and report on the current state of knowledge, and on the strategies to prove it for explicit examples. Then we show how these strategies are pursued and combined with techniques from computational representation theory to prove the abelian defect group conjecture for some of the sporadic simple groups; this is joint work with Shigeo Koshitani and Felix Noeske.