[1] Ions after a local charge exchange with neutral atoms are not controlled anymore by magnetic or electric fields but instead move as neutral atoms with their instantaneous velocities along free-flight trajectories, unless they undergo further collisions of elastic or ionizing types. Atoms originating from a charge exchange process of energetic ions, so-called energetic neutral atoms, can serve as valuable messengers of plasma sites allowing for a remote sensing of distant plasma activities. Remote diagnostics is especially enabled in the case of resonant charge exchange processes at which only charge, but nearly no momentum or energy, is exchanged between collision partners. Most important in this respect and in our context here are charge exchange collisions between protons and hydrogen atoms. In this article we review several theoretical aspects of how this context can be used to study different plasma scenarios like the solar corona and the solar wind, corotating interaction regions, planetary or cometary ionospheres, plasmaspheres or magnetospheres or like the solar wind termination shock, the heliosheath, and the outer heliospheric bow shock. In particular, we address the following questions: Where do energetic atoms play a role, and what kind of role, a dynamic or thermodynamic one, do they play there? From which plasma sites can we expect to receive energetic neutral atom fluxes including even those located far outside these sites? Though we mention in brief presently available and upcoming techniques to measure and to resolve energetic neutral atom fluxes spectrally and spatially, we put the emphasis on theoretical model calculations predicting spectral flux features of energetic neutral atoms with different origins, which in the nearest future may be observed by the NASA Small Explorer mission IBEX and, hopefully, its successors.