  A categorification of a polynomial link invariant is an homological invariant
which contains the polynomial one as its graded Euler characteristic. This
field has been initiated by Khovanov categorification of the Jones polynomial.
Later, P. Ozsvath and Z. Szabo gave a categorification of Alexander polynomial.
Besides their increased abilities for distinguishing knots, this new invariants
seem to carry many geometrical informations. On the other hand, Vassiliev works
gives another way to study link invariant, by generalizing them to singular
links i.e. links with a finite number of rigid transverse double points. The
first part of this thesis deals with a possible relation between these two
approaches in the case of the Alexander polynomial. To this purpose, we extend
grid presentation for links to singular links. Then we use it to generalize
Ozsvath and Szabo invariant to singular links. Besides the consistency of its
definition, we prove that this invariant is acyclic under some conditions which
naturally make its Euler characteristic vanish. This work can be considered as
a first step toward a categorification of Vassiliev theory. In a second part,
we give a refinement of Khovanov homology to restricted links. Restricted links
are link diagrams up to a restricted set of Reidemeister moves. In particular,
closed braids can be seen as a subset of them. Such a refinement give then a
new tool for studying knots and their deformations.
