  We discuss transport experiments for various non-Abelian quantum Hall states,
including the Read-Rezayi series and a paired spin singlet state. We analyze
the signatures of the unique characters of these states on Coulomb blockaded
transport through large quantum dots. We show that the non-Abelian nature of
the states manifests itself through modulations in the spacings between Coulomb
blockade peaks as a function of the area of the dot. Even though the current
flows only along the edge, these modulations vary with the number of quasiholes
that are localized in the bulk of the dot. We discuss the effect of relaxation
of edge states on the predicted Coulomb blockade patterns, and show that it may
suppress the dependence on the number of bulk quasiholes. We predict the form
of the lowest order interference term in a Fabry-Perot interferometer for the
spin singlet state. The result indicates that this interference term is
suppressed for certain values of the quantum numbers of the collective state of
the bulk quasiholes, in agreement with previous findings for other clustered
states belonging to the Read-Rezayi series.
