We recall the definition of the Khovanov homology of links
and mention its modification to odd Khovanov homology. We discuss the fact that in Khovanov homology of links, presence of ℤ2-torsion is a very common phenomenon. We outline the several reasons for this observation (e.g., Hochschild homology of the algebra ℤ[x]/(x2), crucial in Khovanov homology, has only ℤ2 torsion). For other than ℤ2 torsion only a finite number of examples of knots with ℤn-torsion were known, none for n>8. In this talk, we show that there are infinite families of links whose Khovanov homology contains ℤn-torsion for 2 < n < 9 and ℤ2s-torsion for s < 24. We also introduce 4-braid links with ℤ3-torsion which are counterexamples to the PS braid conjecture. We mention that our construction also provides an infinite family of knots with ℤ5-torsion in reduced Khovanov homology and ℤ3-torsion in odd Khovanov homology. Most of our examples are twisted torus knots and links.