This lecture will be centred around the problem of 'uniqueness', i.e. whether the fact that there are many structural models that fit experimental data equally well (within errors) is problem of RMC modeling (and that whether this is problem at all). As an introduction, Reverse Monte Carlo results for amorphous Ni81B19,
liquid sulphur, amorphous silicon and liquid nitrogen, etc... will be discussed; these are 'historical' cases where the easiest-to-obtain RMC results are not (always) physically feasible. The concept of
'constraints' and of 'constrained RMC' will then be introduced. Finally, results from constrained RMC modeling will be presented for amorphous silicon and covalent glasses in general: for this class of materials, constrained RMC can provide arguably the most reliable structural models.