Abstract: The goal of this research is to study the phase behavior and kinetics of order-order (OOT) and order-disorder (ODT) phase transitions in block copolymers in selective solvents. We focus on examining temperature and pressure dependence of the phase diagram and the kinetics of phase transitions using small angle x-ray scattering (SAXS). The kinetics of ODT and OOT was studied for two block copolymer solutions by time-resolved SAXS using temperature ramp and fast quench methods: (i) Poly(styrene- b -isoprene) (PS-PI) diblock copolymer in tetradecane, selective solvent for PI, which displayed face-centered-cubic (FCC) structure at low temperature, body-centered-cubic (BCC) at intermediate temperature, and was disordered at high temperature. Following a quench from 110 C to 50 C, a long-lived meta-stable BCC phase was detected prior to the formation of FCC. The data agrees very well with Cahn's model for nucleation and growth. (ii) Poly(styrene- b -ethylene- co -butylene- b -styrene) triblock copolymer in dibutyl phthaphate, selective solvent for PS, which displayed hexagonally packed cylinders (HEX) at low temperature and lamellar (LAM) phase at high temperatures. This is unusual because in most block copolymer melts LAM occurs at lower temperature than HEX. A geometric model was developed to understand the mechanism of the transition from LAM to HEX. The calculated scattering intensity agrees very well with the experimental data. A pressure network system for SAXS capable of operating in the range of 1-4000 bars with pressure jump capability was built to study the pressure dependence of phase behavior. The system was used to investigate PS-PI diblock copolymer in diethyl phthaphate. The BCC to disorder transition temperature increased with pressure at 20 C/kbar, and the lattice constant increased with pressure. Brownian Molecular Dynamics simulations were carried out to study the phase behavior of multiblock copolymers in a selective solvent. Disordered, BCC, HEX, and LAM phases were obtained depending on the concentration and number of blocks. This research provides detailed information of the kinetics of structural changes in block copolymers in selective solvents. The results provide a good understanding of the mechanism of order-disorder and order-order transitions, and are directly related to industrial applications of block copolymers.