Several computational techniques have been employed to perform an extensive theoretical study of different aspects of ZnS nucleation and growth. First, we use Density Functional Theory and ineratomic potential based calculations to calculate the surface energies for the most common surfaces in the two crystalline phases of ZnS wurzite and sphalerite. This study allows us to calculate the crystal morphologies for both phases, which agree with those observed experimentally. The predicted morphologies correspond to those that crystallites of micrometer sizes would adopt, but in order to understand the nucleation processes we need models for nanoclusters. We therefore use a global minimization technique (simulate annealing), with which we obtain the most stable configuration in vacuum for (ZnS)n clusters, n=10-47, 50, 60, 70 and 80. These clusters are classified into two groups. Clusters with n=10-47, denoted bubble clusters, are hollow structures in which all the atoms are three coordinated. Such structures contrast with the expectation of bulk-like structures in which most of the atoms are four coordinated. Larger (ZnS)n clusters (n=50, 60, 70 and 80) adopt what we have denoted double bubble structures, in which one big bubble encloses a smaller one. The two bubbles are bonded through covalent bonds, therefore creating a network of four coordinated atoms. Density Functional Theory as well as interatomic potential based calculations are employed to calculate the properties of these particles. The thesis concludes with a molecular dynamics study of the nucleation of ZnS in water solution, which reveals that bubble clusters are also formed in the presence of water, and gives insight into the detailed mechanisms of their formation.