This paper provides a summary of recent advances in boron nitride nanotubes (BNNTs) and their composites, including properties, purification, characterization techniques involved, failure modes, and modeling methods. After the discovery of carbon nanotubes, BNNTs were first theoretically predicted and successfully synthesized in 1995 by an arc-discharge method. Following that, other techniques for BNNT synthesis were discovered; however, growing highly purified BNNTs remains difficult. The research on the physical properties of BNNTs shows that they have a stable broadband gap, excellent mechanical strength, high thermal conductivity, and high oxidation resistance. These properties make them a perfect candidate for future nanocomposites for high-temperature applications. Interesting effects of BNNT addition with the resultant mechanical behavior and thermal conductivity in a matrix are observed when BNNTs are applied to form nanocomposites with polymer, metal, and ceramic matrices. Modeling and simulation methods of nanotube composites are highly advantageous in developing BNNT-based nanocomposites. Micromechanics, finite element analysis, and molecular dynamics are modeling techniques used to simulate nanotubes and are crucial for model- informed manufacturing and design. In summary, modeling, synthesis, purification, characterization, and properties of BNNT composites are all reviewed in this paper.