Block copolymers have been extensively studied due to their ability to spontaneously self-organize into a wide variety of morphologies that are valuable in energy-, medical-, and conservation-related (nano)technologies. While the phase behavior of bicomponent diblock and triblock copolymers is conventionally governed by temperature and individual block masses, it is demonstrated here that their phase behavior can alternatively be controlled through the use of blocks with random monomer sequencing. Block random copolymers (BRCs), i.e., diblock copolymers wherein one or both blocks are a random copolymer comprised of A and B repeat units, have been synthesized, and their phase behavior, expressed in terms of the order-disorder transition (ODT), has been investigated. The results establish that, depending on the block composition contrast and molecular weight, BRCs can microphase-separate. We also report that large variation in incompatibility can be generated at relatively constant molecular weight and temperature with these new soft materials. This sequence-controlled synthetic strategy is extended to thermoplastic elastomeric triblock copolymers differing in chemistry and possessing a random-copolymer midblock.