Dynamical and convective instabilities are two mechanisms that contribute significantly to the dissipation of larger-scale motions and the generation of turbulence in the middle atmosphere. The former are normally due to enhanced velocity shears and/or a local minimum of the static stability either in the mean flow or associated with low-frequency wave motions. The most common dynamical instability is the Kelvin-Helmholtz (KH) instability which is often manifested in the atmosphere as a series of KH billows. Convective instabilities occur where the lapse rate becomes superadiabatic through the action of gravity waves and appear to predominate for high-frequency wave motions. This paper reviews the theory and the observational evidence for both types of instabilities in the lower and middle atmosphere.