  Quarks whose left- and right-handed chiral components are both singlets with
respect to the SU(2) weak-isospin gauge group, offer interesting physics
possibilities beyond the Standard Model (SM) already studied in many contexts.
We here address some further aspects. We first collect and update the
constraints from present data on their masses and mixings with conventional
quarks. We discuss possible effects on $b\to s\gamma$ and $Z\to b\bar b$ decays
and give fresh illustrations of CP asymmetries in $B^0$ decays differing
dramatically from SM expectations. We analyse singlet effects in grand
unification scenarios: $d$-type singlets are most economically introduced in
${\bf 5+5^*}$ multiplets of $SU(5)$, with up to three generations, preserving
gauge coupling unification with perturbative values up to the GUT scale;
$u$-type singlets can arise in ${\bf 10+10^*}$ multiplets of $SU(5)$ with at
most one light generation. With extra matter multiplets the gauge couplings are
bigger; we give the two-loop evolution equations including exotic multiplets
and a possible extra $U(1)$ symmetry. Two-loop effects can become important,
threatening unification (modulo threshold effects), perturbativity and
asymptotic freedom of $\alpha_3$. In the Yukawa sector, top-quark fixed-point
behaviour is preserved and singlet-quark couplings have infrared fixed points
too, but unification of $b$ and $\tau$ couplings is not possible in a
three-generation $E_6$ model.
