The first part of this paper contains a thorough exposition of the
proof of the classification of topologically trivial Legendrian knots
(i.e., Legendrian knots bounding embedded 2-disks) in tight contact
3-manifolds. These techniques were never published in detail when the
classification result was announced over ten years ago. The final part of
the present paper contains a systematic discussion of Legendrian knots
in overtwisted contact manifolds, and in particular, gives the coarse
classification (i.e., classification up to a global contactomorphism) of
topologically trivial exceptional Legendrian knots in overtwisted contact
$S^3$ according to the values of the invariants tb, r. We show, moreover,
that such knots only occur for one of the infinitely many overtwisted
contact structures on $S^3$. We remark that our tight classification
result also implies that any topologically trivial loose Legendrian knots
with same value of (tb, r) in an overtwisted contact 3-manifold are in
fact Legendrian isotopic if $tb < 0$.