Any negative definite plumbed 3-manifold has its lattice cohomology, determined from the lattice of one of its plumbing representations. I will present several properties of the these modules, e.g., the `reduction theorem', which reduced the rank of the lattice to the number of `bad vertices'. Furthermore, I will define a modified version of the theory, called `path lattice cohomology'. I will discuss its motivation and connection with the theory of surface singularities.