  The quantum phase transition between two clean, non interacting topologically
distinct gapped states in three dimensions is governed by a massless Dirac
fermion fixed point, irrespective of the underlying symmetry class, and this
constitutes a remarkably simple example of superuniversality. For a
sufficiently weak disorder strength, we show that the massless Dirac fixed
point is at the heart of the robustness of superuniversality. We establish this
by considering both perturbative and nonperturbative effects of disorder. The
superuniversality breaks down at a critical strength of disorder, beyond which
the topologically distinct localized phases become separated by a delocalized
diffusive phase. In the global phase diagram, the disorder controlled fixed
point where superuniversality is lost, serves as a multicritical point, where
the delocalized diffusive and two topologically distinct localized phases meet
and the nature of the localization-delocalization transition depends on the
underlying symmetry class. Based on these features we construct the global
phase diagrams of noninteracting, dirty topological systems in three
dimensions. We also establish a similar structure of the phase diagram and the
superuniversality for weak disorder in higher spatial dimensions. By noting
that $1/r^2$ power-law correlated disorder acts as a marginal perturbation for
massless Dirac fermion in any spatial dimension $d$, we have established a
general renormalization group framework for addressing disorder driven critical
phenomena for fixed spatial dimension $d > 2$.
