The formation process of dust grains around cool stars and the dust processing in the interstellar space are reviewed. Infrared spectral characteristics of circumstellar dust grains indicate that newly-formed grains are not in a highly crystalline state, but they are rather amorphous material. The dust formation process in circumstellar regions must involve kinematic aspects to a large degree. On the other hand, theoretical investigations suggest that the destruction process of dust grains in the interstellar space is quite rapid compared to the supply rate from stellar sources. Therefore, a large fraction of dust grains must be forming also in the interstellar space. Very few investigations have been attemped on the formation of solid particles under the interstellar harsh conditions, but they will be essential in the study of interstellar dust.
