In this work we introduce two models to understand the anomalous composition dependence of viscosity of binary mixtures. Both models consist of a mixture of two molecular species (A and B) with the same diameter and mass but varying solute-solvent Lennard-Jones interaction. In model I, the two different species are strongly attractive while in model II, the attraction is weaker than that between the pure components. We have carried out extensive computer simulations of the two models. In addition, we study mode coupling theory for the viscosity of binary mixtures. Both the molecular dynamics simulations and the microscopic theory show the emergence of strong nonideality even in such simple systems. Model I shows a positive departure from ideality while model II shows the reverse behavior. The reason can be traced to the enhanced mean square stress fluctuations (MSSF) in the model I but decreased MSSF in the model II. The models show deviations (from ideality) very similar to the ones observed in experiments.