The structure and stability of colloidal monolayers depends crucially on the effective pair interaction potential between colloidal particles. In the first part of the thesis, we present two novel methods for extracting the pair potential from the two-dimensional radial distribution function of dense colloidal monolayers. The first is a so-called Predictor-Corrector routine that replaces the conventionally unknown Bridge function, with an iteratively obtained hard-disk bridge function. The second method is based on the Ornstein-Zernike relation and the HMSA closure that contains a single fitting parameter which is determined by requiring thermodynamic consistency between the virial and compressibility equations of state. The accuracy of these schemes are tested against Monte Carlo simulation data from monolayers interacting via a wide range of commonly encountered pair potentials. We also test the stability of these methods with respect to noise levels and truncation of the source data to mimic experimentally obtained structural data. Finally we apply these inversion schemes to experimental pair correlation function data obtained for charged polystyrene particles adsorbed at an oil/water interface. We find that the pair interaction potential is purely repulsive at low densities, but an attractive component develops at higher densities. The origin of this attractive component at higher densities is at present unknown.In the second part of this thesis, we study how the colloid interactions studied above influence the structure of the colloidal monolayer. Specifically inspired by recent experimental results on mixed monolayers of large and small very hydrophobic silica particles at an octane/water interface, we study theoretically the structure of two-dimensional binary mixtures of colloidal particles interacting via a dipole-dipole potential. We find that at zero temperature, a rich variety of binary crystal structures are obtained whose structure depends on the dipole moment ratio and the number fraction of small particles. At experimentally relevant finite temperatures, we find that the AB2 and AB6 binary super-lattice structures are thermodynamically stable while other binary structures e.g. AB5, which are stable at zero temperature, are thermodynamically unstable at finite temperature. Specifically, the melting temperature of the AB5 system is found to be three orders of magnitude lower than that of the AB2 and AB6 systems and at experimentally relevant temperatures, melts into a semi-disordered phase with local AB6 order.