  The paper develops a general theory of orderability of quandles with a focus
on link quandles of tame links and gives some general constructions of
orderable quandles. We prove that knot quandles of many fibered prime knots are
right-orderable, whereas link quandles of most non-trivial torus links are not
right-orderable. As a consequence, we deduce that the knot quandle of the
trefoil is neither left nor right orderable. Further, it is proved that link
quandles of certain non-trivial positive (or negative) links are not
bi-orderable, which includes some alternating knots of prime determinant and
alternating Montesinos links. The paper also explores interconnections between
orderability of quandles and that of their enveloping groups. The results
establish that orderability of link quandles behave quite differently than that
of corresponding link groups.
