This work aims at developing a fundamental understanding of how shape of nano/micro-particles affects their thermodynamic phase behavior and dynamic properties. Anisotropic interaction fields encoded in nanoparticles of nonspherical shape can drive their assembly into many complex, ordered or partially ordered structures ("mesophases"). Some of these self-assembled 'phases' are highly desirable for their distinctive electronic, physical and optical properties and are very sensitive to the entropic interactions of their building blocks and other external driving fields. To understand the basic principles controlling formation of these assemblies, we performed systematic simulation studies to explore the effect of 'shape' or excluded volume interactions on the equilibrium mesophase behavior and on selected non-equilibrium mechanical properties of these systems. Monte Carlo simulations performed on a class of spacefilling polyhedral shapes predict formation of various novel liquid-crystalline (LC) and plastic-crystalline phases. By correlating these results with particle anisotropy and rotational symmetry, guidelines for predicting phase behaviour of polyhedral particles are proposed. The effect of quenched size polydispersity on the phase behavior of polyhedral particles is also elucidated by carrying out extensive compression Monte Carlo simulation for polydisperse systems of three distinct shapes. High polydispersities are found to lead to an increased stability of mesophases and the formation of jammed states at high densities. To investigate the effect of anisotropy on dynamics, we performed non-equilibrium molecular dynamics simulations to chart the yielding and shear induced melting behavior of mixed crystalline assemblies of spherical and dimer-shaped particles. Important differences in microstructure, dislocations and stress relaxation behavior emerge with introduction of this shape perturbation (dimer particles), which manifests as non- monotonic yield stress values and a two-stage shear melting behavior. Altogether this work makes some inroads toward a general understanding and taxonomy of the effect of particle shape on the thermophysical properties of colloidal assemblies.