The polymers of 3, 3-diazidomethyloxetane (BAMO) are typical high-energy and high-density energetic polymers. The development of synthesizing BAMO monomer, BAMO homopoymer and copolymers was reviewed, and future study about them was also prospected in this paper. BAMO-AMMO and BAMO-GAP energetic thermoplastic elastomers are widely used. Cation livng polymerization is major synthesizing method of BAMO polymers.