<p>The microphase segregation behavior, which exhibits periodic patterns on a mesoscale, has been found in many systems where it has demonstrated its extreme industrial usefulness in the diblock copolymer system. When studying more general isotropic colloidal systems, periodic microphases should ubiquitously emerge in systems for which short-range inter-particle attraction is frustrated by long-range repulsion~(SALR). The morphological richness of these phases makes them desirable material targets, but our relatively coarse understanding of even simple models hinders controlling their assembly both from thermodynamic and dynamic points of view. The thermodynamic question is what should be the appropriate potential to stabilize microphases, such as cluster crystal, cylindrical, double gyroid and lamellar, while the dynamic question is whether the current experiments are long enough for these phases to appear. This dissertation will focus on solving these two parts of problems and hopefully guide the experiments to discover a simple material that can have microphase segregation behavior. In order to answer the thermodynamic problem of the stability of the microphases, we use a novel thermodynamic integration method as well as density functional methods in comparing the free energy of the microphases with uniform liquids. With the thermodynamic integration, we locate FCC-cluster, cylindrical, double gyroid and lamellar phases as well as nontrivial interplay between cluster, gel and microphase formation for a model microphase former. We also extended the methods to the model with a shorter and longer repulsion region where we found that the shorter region of the system may be in the Wigner glass of clusters of different sizes rather than the microphases. We also compare our simulation results with that from the density functional theory where we demonstrate that the classical density functional theory is qualitatively right but the simple improvement of the radial distribution functional by assuming the system is the same as Percus-Yevick hard sphere does not make a quantitatively difference. Our finding confirms that if the colloidal system has proper SALR potential as well as the right regime of area fraction and temperature, the microphase will be found in these systems. We then answer the second question which is whether the slow dynamics hinders the formation of microphases. We study the modeled microphase former and track the change of the first peak in the structure factor as well as the structural correlation time. We found that the system has a very complex dynamical regimes, including homogeneous fluid, void micelle, liquid gel and solid gel. The system becomes extreme slow in the solid gel regime but if in the regime that density and temperature are near the order-disorder transition, the lamellar self-assembly is much faster than the relaxation time of the solid gel which may explain why in the experimental system, the colloids seem stuck forever. We have collaborated with an experimental group to realize the SALR self-assemble behavior in a well controlled system. We have calibrated the system using a high precision thermodynamic integration by determining and matching the critical point and triple point of the experiments when the system is set up in the purely attractive regime. The system, however, becomes unpredictable when it goes into the SALR system where both higher body and other interactions become dominant. Finally, we try to extend our system to a spherocylinder model, which is an anisotropic particles with SALR. We have developed a novel cell list method here to accelerate the simulation. By determining the percolation transition and the order parameter, we find that the simple anisotropic interaction will introduce a much complex phase behavior of the system even in the disordered regime. We have identified several disordered phases, including homogeneous liquid, micellar liquid, free rotator gel, nematic gel and smectic gel.</p> / Dissertation