This thesis presents a comprehensive computational study of the bulk and surface properties of two major iron-bearing minerals: hematite (α-Fe2O3) and mackinawite (tetragonal FeS), and subsequently unravels the interactions of a number of environmentally important molecules with the low-Miller index surfaces of these iron-bearing minerals using a state-of-the-art methodology based on the density functional theory (DFT) techniques. First, we have used the Hubbard corrected DFT (GGA+U) calculations to unravel the interactions of a single benzene molecule with the (0001) and (01 2) surfaces of α-Fe2O3 under vacuum conditions. α-Fe2O3 is correctly described as a charge-transfer insulator, in agreement with the spectroscopic evidence when the optimized value for U = 5 eV is employed. The benzene molecule is shown to interact relatively more strongly with the (01 2) surface via cation-π interactions between the π-electrons of benzene ring and the surface Fe d-orbitals than with the (0001) where van der Waals interactions are found to play important role in stabilizing the molecule at the surface. In the second part of this thesis, DFT calculations with a correction for van der Waals interactions (DFT-D2 scheme of Grimme) have been used to simulate the bulk properties, surface structures and reactivity of layered mackinawite (FeS). We demonstrate that the inclusion of van der Waals dispersive interaction sensibly improves the prediction of interlayer separation distance in FeS, in good agreement with experimental data. The effect of interstitial impurity atoms in the interlayer sites on the structure and properties of FeS is also investigated, and it is found that these contribute considerably to the mechanical stability of the FeS structure. From the geometry optimization of the low-Miller index surfaces of FeS, we have shown the (001) surface terminated by sulfur atoms is by far the most energetically stable surface of FeS. The calculated surface energies are used successfully to reproduce the observed crystal morphology of FeS. As an extension to the surface studies, we have used the DFT-D2 method to model the adsorption mechanism of arsenious acid (As(OH)3), methylamine (CH3NH2) and nitrogen oxides (NO and NO2) molecules on the low-Miller index FeS surfaces under vacuum conditions. The As(OH)3 molecule is demonstrated to preferentially form bidentate adsorption complexes on FeS surfaces via two O‒Fe bonds. The calculated long As−Fe and As−S interatomic distances (> 3 Å) clearly suggest interactions via outer sphere surface complexes with respect to the As atom, in agreement with the experimental observations. The growth modifying properties of methylamine, the capping agent used in the synthesis of FeS, are modelled by surface adsorption. The strength of the interaction of CH3NH2 on the different FeS surfaces is shown to increase in the order: (001) < (011) < (100) < (111) and an analysis of the nature of bonding reveals that the CH3NH2 molecule interacts preferentially with the surface Fe d-orbitals via the lone-pair of electrons located on the N atom. Our simulated temperature programmed desorption process shows that methylamine is stable up to about 180 K on the most reactive (111) surface, which is comparable to the experimental desorption temperatures predicted at metallic surfaces. Finally, the catalytic properties of FeS as a nanocatalyst for the adsorption, activation and decomposition of environmentally important NOx gases have been explored, where we consider the nature of binding of the NOx species to the FeS surfaces and their dissociation reaction mechanisms