  We present the local classification of singularities of smooth vector fields
on the line, with respect to the equivalence relation of $C^1$--conjugacy.
Along the way, we recall the analogous classification, up to $C^0$ and
$C^{\infty}$ conjugacy. We also give the transversal unfoldings of the
corresponding normal forms and treat the case where the changes of coordinates
are tangent to the identity. Thus, a fairly complete description of the $1$--d
case is achieved.
