We start with a brief introduction into knot homology theories and categorification of polynomial knot invariants. In particular, we review the construction and the basic properties of a new homological knot invariant, recently introduced by Khovanov and Rozansky. To every knot diagram, it associates a bigraded chain complex whose graded Euler characteristic is the quantum-group sl(N) invariant. Motivated by the ideas from physics, we then present a reformulation of the sl(N) knot homology in terms of new triply-graded knot invariants. This leads to new conjectures on the structure of the homological knot invariants and suggests a larger theory which unifies the HOMFLY polynomial, the Khovanov Rozansky homology, and the knot Floer homology of OzsvathSzabo-Rasmussen. We also describe the geometric meaning of the new knot invariants in terms of the enumeration geometry of Riemann surfaces with boundaries in a certain Calabi-Yau three-fold.