  We characterise the Morita equivalence classes of blocks with extraspecial
defect groups $p_+^{1+2}$ for $p \geq 5$, and so show that Donovan's conjecture
and the Alperin-McKay conjecture hold for such $p$-groups. For $p=3$ we reduce
Donovan's conjecture for blocks with defect group $3_+^{1+2}$ to bounding the
Cartan invariants for such blocks of quasisimple groups. We apply the
characterisation to the case $p=5$ as an example, to list the Morita
equivalence classes of such blocks.
