I review recent progress in experimental studies on morphology transitions of ordered microdomains in block copolymers and their kinetics, which have been studied using, respectively, static and time-resolved small-angle X-ray scattering (SAXS) techniques with synchrotron radiations, and using the transmission electron microscopy (TEM), as well. The samples used are some polystyrene-block-polyisoprene (SI) diblock copolymers having various compositions, a polystyrene-block-polybutadiene-block-polystyrene (SBS) triblock copolymer and a polystyrene-block-(hydrogenated polybutadiene)-block-polystyrene (SEBS). For the SI samples, thermoreversible morphology transitions are discussed. The thermodynamically stable morphologies were carefully examined for both the pure SI sample and the binary mixtures of the SI samples with different styrene/isoprene compositions. The reason of employing the binary mixtures are to control net styrene/isoprene compositions without synthesis. For the pure SI diblock copolymer, we could observe reversible morphological transition between cylinders and spheres at lower and higher temperatures, respectively. For the SBS and SEBS samples, I discuss casting-solvent assisted nonequilibrium morphologies and thermally induced morphological transition into equilibrium ones. Here, a selective solvent, i.e., good for one-component block chains but poor for another component block chains, plays an important role upon formation of the nonequilibrium morphologies during casting process where the solvent gradually evaporates. The reason why we could freeze the non-equilibrium morphologies in the as-cast bulk film is attributed to vitrification of the polystyrene (PS) phase. Therefore, once the samples are heated up to above the glass transition temperatures of the PS phase, the PS chains can move to attain equilibrium and, in turn, the morphologies change. The SBS was subjected to the transition from cylinders to lamellae, whereas the SEBS suffered the transition from lamellae to cylinders. For these transitions, kinetic studies were also conducted in order to reveal transition processes. The results of the time-resolved SAXS studies provided useful information to consider the transition mechanism.