Interstellar dust is an intrinsic component of the interstellar medium and plays an important role in many astrophysical processes, including gas heating and cooling, and the formation of planets and stars. Interstellar dust grains are present in a wide range of sizes, from Angstrom (e.g., big molecules) to micron. The alignment of dust grains with magnetic fields enables dust as a powerful tool to probe magnetic fields from the diffuse cloud to star-forming regions to protoplanetary disks. In this review, I will review our modern understanding of properties of interstellar dust, focusing on two important aspects, namely dust polarization and microwave emission from rapidly spinning dust nanoparticles (aka spinning dust emission). First, I will review observational properties of interstellar dust in our Galaxy, including dust extinction, emission, and polarization. Second, I will talk about astrophysics of dust polarization, including grain alignment theory and applications of dust polarimetry for dust properties, star formation and cosmic inflation studies. Finally, I will discuss microwave emission from spinning nanoparticles (polycyclic aromatic hydrocarbons, silicate and iron nanoparticles), and its implication for probing nanoparticles in the entire protoplanetary disks.