We survey quite extensively the present research status of ion-stopping in dense plasmas of potential importance for initial confinement fusion (ICF) driven by intense and heavy ion beams, and also for warm dense matter (WDM). First, we put emphasis on every possible mechanism involved in the shaping of the ion projectile effective charge, while losing energy in a target plasma with classical ions and partially degenerate electrons. Then, we switch to ion stopping by target bound electrons, taking detailed account of mean excitation energies. Free electron stopping has already been given a lot of attention in former works [C. Deutsch et al., Recent Res. Devel. Plasma 1 (2000) 1-23; Open Plasma Phys. J. 3 (2010) 88-115]. Then, we extend the usual standard stopping model (SSM) framework to nonlinear stopping including a treatment of the Z3 Barkas effect and a confronting comparison of Bloch and Bohr Coulomb logarithms. Finally, we document low velocity ion slowing down (LVISD) in single ion plasmas as well as in binary ionic mixtures (BIM), in connection with specific ICF fuels.