We present an overview of a numerical study on the small-scale dynamics and the large-scale dispersion of small inertial particles in stably stratified turbulence. Three types of particles are examined: fluid particles, light inertial particles (with particle-to-fluid density ratio 1=¿p/¿f = 25) and heavy inertial particles (¿p/¿>>f1). Stratification suppresses the vertical dispersion of all three types of particles compared to isotropic turbulence. The horizontal dispersion, on the other hand, is enhanced. The importance of the hydrodynamic forces, which act on (light) inertial particles and directly affect the small-scale dynamics of the particles, is examined for particles with ¿p/¿f in the range from 1 to 25. These results primarily concern the forces on light particles in homogeneous isotropic turbulence, as at small scales in weakly stratified turbulence isotropy is almost restored. The effect of the presence of a density stratification on the particle dynamics is thus assumed to be almost negligible, which is supported by the similarity of the results from computations of the forces on small inertial particles in homogeneous isotropic turbulence and in weakly stratified turbulence. The inertia of the particles results in a non-uniform particle distribution over the domain. This preferential concentration effect is briefly reviewed here for heavy particles, and it is found that the effect is stronger in isotropic turbulence than in stratified turbulence. It is shown that preferential concentration also occurs for light inertial particles in homogeneous isotropic turbulence.