[en] As now being explored for fusion applications confinement systems based on the mirror principle embody two kinds of plasma regimes. These two regimes are: (a) high-beta plasmas, stabilized against MHD and other low frequency plasma instabilities by magnetic-well fields, but characterized by non-Maxwellian ion distributions; (b) near-Maxwellian plasmas, confined electrostatically (as in the tandem mirror) or in a field-reversed region within the mirror cell. Common to both situations are the questions of anomalous transport owing to high frequency instabilities in the non-maxwellian portions of the plasmas. This report will summarize the status of theory and of experimental data bearing on these questions, with particular reference to the high temperature regimes of interest for fusion power