Bottlebrush block copolymers are polymers with chemically distinct polymer side chains grafted onto a common backbone. The unique architecture induced properties make these materials attractive for applications such as photonic materials, stimuli responsive actuators and drug delivery vehicles to name a few. This dissertation primarily investigates the phase transitions and rheological behavior of amorphous-crystalline bottlebrush brush block copolymers and their composites. The temperature induced phase behavior is investigated using time resolved synchrotron X-ray source. Irrespective of volume fraction and backbone length, the samples display strong segregation even at high temperatures (200 °C) and there is no accessible order-disorder transition in the temperature range of 25-200 °C. The isothermal crystallization kinetics reveal a two-stage crystallization process, different than that observed in linear block copolymers. A considerable part of this dissertation is focused on the study of the effect of hydrogen bonding additives on the relaxations of brush block copolymer. The additives greatly enhance the mechanical and physical properties of the pristine polymer. The small molecules also impart a gel-like characteristic due to the formation of physically crosslinked network. Finally, the understanding of the brush block copolymer systems from the previous studies and literature is used to study the self-assembly of nanorods using brush block copolymers as templates.