  Given an inaccessible J\'onsson cardinal $\lambda$, a sequence of results due
to Shelah from Cardinal Arithmetic and Sh413 tell us that $\lambda$ must be at
least $\lambda\times\omega$-Mahlo. We may then ask ourselves whether we can
improve this bound, and unfortunately not much progress has been made on this
question since Sh413. Part of the problem may be that the proofs involved are
rather complicated and make use of somewhat ad hoc machinery. In order to
remedy this, we present a survey and new proofs of these results regarding the
Mahlo degree of an inaccessible J\'onsson cardinal with the hope of making this
material accessible.
