Block copolymers are a class of soft matter that self-assemble to form ordered morphologies on the scale of nanome- ters, making them ideal materials for various applications. These applications directly depend on the shape and size of the self-assembled morphologies, and hence, a high degree of control over the self-assembly is desired. Grafting block copolymer chains onto a substrate to form copolymer brushes is a versatile method to fabricate functional surfaces. Such surfaces demonstrate a response to their environment, i.e., they change their surface topography in response to different external conditions. Furthermore, such surfaces may possess nanoscale patterns, which are important for some applica- tions; however, such patterns may not form with spun-cast films under the same condition. In this review, we summarize the recent progress of the self-assembly of block copolymers grafted onto a flat substrate. We mainly concentrate on the self-assembled morphologies of end-grafted AB dibloek eopolymers, junction p0int-grafted AB diblock copolymers （i.e., Y-shaped brushes）, and end-grafted ABA triblock copolymers. Special emphasis is placed on theoretical and simulation progress.
