After an initial degree in engineering, a Master of Science and then a PhD in hydrodynamics, I joined CEA in 1993 to work on hydrodynamic instabilities in flows of inertial confinement fusion (ICF), and more specifically on the linear regime of these instabilities. This work has focused on devising approaches that are global, in time and space, in order to be predictive, given the strong unsteadiness and heterogeneity of such flows. These approaches, necessarily numerical, rely on the approximation, classical in this field, of radiation hydrodynamics. A first approach has led to a numerical code for computing the amplification of three-dimensional linear perturbations about one-dimensional base flows with spherical or planar symmetry, aiming at applications to ICF capsule implosions up to the onset of thermonuclear reactions. A second approach, more specific, deals with the linear stability of self-similar planar base flows representative of the early stage of ICF capsule implosions. This approach goes beyond mere amplification computations in that it implements methods of non-modal stability theory for unsteady flows, the sole capable of giving stability results for such flows and, in particular, of identifying perturbation transient growths.