This thesis investigates the properties of exciton states in semiconductor nanocrystals using effective mass models. We focus on type-I core-shell nanocrystals in which the staggered band alignments of the core and shell material mean the lowest energy states for electrons and holes lie in different spatial regions, giving rise to spatially indirect excitons. The technological potential of type-I! nanocrystals provides motivation for understanding single exciton states which determine many important optical properties. In the first research chapter we study CdTe/CdSe and CdSe/CdTe nanocrystals using a single-band and (2,6)-band effective mass model. The (2,6)-band model is based on a multiband k·p theory previously developed for spherical quantum dot heterostructures. We calculate exciton energies as a function of the core radius a and shell width as of the heterostructure, and assign six exciton transitions in the experimental absorption spectra of CdTe/CdSe nanocrystals. The second research chapter is concerned with strained ZnTe/ZnSe nanocrystals. The (2,6)-band model is modified to incorporate strain using a continuum elasticity model. Exciton energies from absorption spectra are compared with the predictions of the strained and unstrained nanocrystal models, showing that they only describe the lowest exciton energy of one of the three size series. Improved agreement is found for the change in exciton energy due to a particular shell width, with the strained nanocrystal model giving much better fits to the as-dependence. The as-dependence of nanocrystals with alloyed heterointerfaces is better described by the unstrained nanocrystal model, indicating alloying relaxes the strain in this system. In the final chapter we model spatial correlations between the electron and hole in CdTe/CdSe and CdSe/CdTe nanocrystals using a configuration interaction approach developed in the framework of the (2,6)-band k·p theory. We find that the single-particle basis can, be restricted without changing t~e resulting exciton energies significantly; using this decoupled configuration ihter~ction approach we calculate exciton energy shifts due to correlation as a function of aand as. Dielectric confinement increases correlation for many heterostructure designs by shifting carrier wavefunctions away from the surface, and the interparticle Coulomb interaction leads to large changes in radial probability density for the uniform dielectric constant case. Dielectric confinement affects the correlated hole more than the electron so that excitons in the CdSe/CdTe heterostructure are more affected by the dielectric environment than those in the CdTe/CdSe heterostructure. The overall behaviour of the correlated charge density is due to the net effect of the type-I! spatial confinement, interparticle Coulomb attraction, dielectric confinement and single-particle electronic structure.