Dust is an essential component of the interstellar medium (ISM) and plays an important role in many different astrophysical processes and phenomena. Traditionally, dust grains are known to be destroyed by thermal sublimation, Coulomb explosions, sputtering, and shattering. The first two mechanisms arise from the interaction of dust with intense radiation fields and high-energy photons (extreme UV), which work in a limited astrophysical environment. The present review is focused on a new destruction mechanism present in the dust-radiation interaction that is effective in a wide range of radiation fields and has ubiquitous applications in astrophysics. We first describe this new mechanism of grain destruction, namely rotational disruption induced by Radiative Torques (RATs) or RAdiative Torque Disruption (RATD). We then discuss rotational disruption of nanoparticles by mechanical torques due to supersonic motion of grains relative to the ambient gas, which is termed MEchanical Torque Disruption (METD). These two new mechanisms modify properties of dust and ice (e.g., size distribution and mass), which affects observational properties, including dust extinction, thermal and nonthermal emission, and polarization. We present various applications of the RATD and METD mechanisms for different environments, including the ISM, star-forming regions, astrophysical transients, and surface astrochemistry.