Morita Frobenius numbers were introduced by Radha Kessar in 2004 in the context of Donovan’s Conjecture in block theory. The Morita Frobenius number of an algebra is the number of Morita equivalence classes of its Frobenius twists. I will present results from joint work with Radha Kessar where we aim to bound the Morita Frobenius numbers of blocks of quasi-simple finite groups. I will explain the connection to Donovan's Conjecture, and illustrate how recent results of Bonnafé-Dat-Rouquier play a crucial role in our methods.