  It is a prominent conjecture (relating Riemannian geometry and algebraic
topology) that all simply-connected compact manifolds of special holonomy
should be formal spaces, i.e., their rational homotopy type should be derivable
from their rational cohomology algebra already -- an as prominent as particular
property in rational homotopy theory. Special interest now lies on exceptional
holonomy $G_2$ and $Spin(7)$. In this article we provide a method of how to
confirm that the famous Joyce examples of holonomy $G_2$ indeed are formal
spaces; we concretely exert this computation for one example which may serve as
a blueprint for the remaining Joyce examples (potentially also of holonomy
$Spin(7)$). These considerations are preceded by another result identifying the
formality of manifolds admitting special structures: we prove the formality of
nearly K\"ahler manifolds. A connection between these two results can be found
in the fact that both "special holonomy" and "nearly K\"ahler" naturally
generalize compact K\"ahler manifolds, whose formality is a classical and
celebrated theorem by Deligne-Griffiths-Morgan-Sullivan.
