Abstract: The main goal of this dissertation is to study the phase behavior and kinetics of cylinder to sphere phase transition in block copolymers in selective solvents using time- resolved small angle x-ray scattering (SAXS), rheology, Atomic Force Microscopy (AFM), modeling and simulation. Block copolymers consist of two or more chemically distinct polymer blocks connected by a covalent bond. The incompatibility of the constituent blocks leads to phase separation on length scales of 10-1000 nm instead of bulk phase separation. The addition of a selective solvent which preferentially solubilizes one of the components further enriches the phase behavior and provides easier control over the morphology of micellar domains. Although many studies have been made on the phase diagrams of block copolymer solutions the kinetics of phase transitions between two different crystalline symmetries are less understood. The experiments were conducted on a triblock copolymer of poly(styrene- b -ethylene- co -butylene- b -styrene) (SEBS), in mineral oil, a solvent selective to middle EB block. AFM measurements clearly showed the cylindrical micelles arranged hexagonally (HEX) at 110°C. Synchrotron based time-resolved SAXS measurements showed that the transition from HEX to spherical micelles arranged on body-centered cubic (BCC) lattice occurs via a nucleation and growth mechanism for shallow temperature jumps and via spinodal decomposition for deep temperature jumps. We developed a geometrical model of coupled anisotropic fluctuations to calculate the scattering and found very good agreement with the SAXS data. Brownian Molecular Dynamics simulations were carried out to provide microscopic insights on the HEX to cubic transition. HEX, face-centered cubic (FCC), lamellar, and hexagonally perforated lamellar ordered phases were obtained depending on the concentration, temperature and solvent selectivity. Kinetics of HEX to FCC was examined by quenching the temperature or rapidly changing the well-depth of the Lennard-Jones potential used in the simulation. The observations from snapshots, density profiles and calculated scattering intensity all agree well with the nucleation and growth mechanism. This work provides a detailed understanding of the mechanism and kinetics of phase transition of cylinders to spheres in block copolymer solution system. The results have relevance to block copolymer processing and other applications.