In this feature article, we briefly review the new methods we have utilized recently in the investigation of morphology and phase behavior of block copolymers. We first describe the chromatographic fractionation method to purify block copolymers from their side products of mainly homopolymers or block copolymer precursors inadvertently terminated upon addition of the next monomer in the sequential anionic polymerization. The chromatographic method is extended to the fractionation of the individual block of diblock copolymers which can yield the diblock copolymer fractions of different composition and molecular weight, which also have narrower distributions in both molecular weight and composition. A more detailed phase diagram could be constructed from the set of block copolymer fractions without the need of acquiring many block copolymers each prepared by anionic polymerization. The fractions with narrow distribution in both molecular weight and composition exhibit better long-range ordering and sharper phase transition. Next, epitaxial relationships between two ordered structures in block copolymer thin film is discussed. We employed the direct visualization method, transmission electron microtomography(TEMT) to scrutinize the grain boundary structure.