A novel and efficient methodology is developed for computer simulations of realistic two-dimensional (2D) and three-dimensional (3D) microstructures. The simulations incorporate realistic 2D and 3D complex morphologies/shapes, spatial patterns, anisotropy, volume fractions, and size distributions of the microstructural features statistically similar to those in the corresponding real microstructures. The methodology permits simulations of sufficiently large 2D as well as 3D microstructural windows that incorporate short-range (on the order of particle/feature size) as well as long-range (hundred times the particle/feature size) microstructural heterogeneities and spatial patterns at high resolution. The utility of the technique has been successfully demonstrated through its application to the 2D microstructures of the constituent particles in wrought Al-alloys, the 3D microstructure of discontinuously reinforced Al-alloy (DRA) composites containing SiC particles that have complex 3D shapes/morphologies and spatial clustering, and 3D microstructure of boron modified Ti-6Al-4V composites containing fine TiB whiskers and coarse primary TiB particles. The simulation parameters are correlated with the materials processing parameters (such as composition, particle size ratio, extrusion ratio, extrusion temperature, etc.), which enables the simulations of rational virtual 3D microstructures for the parametric studies on microstructure-properties relationships. The simulated microstructures have been implemented in the 3D finite-elements (FE)-based framework for simulations of micro-mechanical response and stress-strain curves. Finally, a new unbiased and assumption free dual-scale virtual cycloids probe for estimating surface area of 3D objects constructed by 2D serial section images is also presented.