Results on several topics concerning the symmetry and the stability of the implosion of heavy ion fusion inertial confinement fusion (ICF) targets are reported. By means of 2-D radiation-hydrodynamics simulations, it is shown that some direct-drive targets are subjected, during acceleration, to rather violent Rayleigh-Taylor instabilities. Radiation generation, confinement and symmetrization in some hohlraum targets for indirect-drive ICF, including cylindrical radiation converters is studied by 2-D and 3-D codes. It appears that at least six converters are needed to provide adequate radiation symmetrization and efficient radiation coupling to the fusion capsule. A new concept of radiation driven targets, including a spherically symmetric converter is presented. In the final section, some results are given on high resolution 2-D studies of the turbolent mixing induced by the Rayleigh-Taylor instability.