Using a microscopic antikaon-nucleus optical potential recently developed by Ramos and Oset [10] from a chiral model, we calculate strong interaction energy shifts and widths for K- atoms. This purely theoretical potential gives an acceptable description of the measured data (chi(2)/num.data = 3.8), though it turns out to be less attractive than what can be inferred from the existing kaon atomic data. We also use a modified potential, obtained by adding to the latter theoretical one a s-wave term which is fitted to known experimental kaonic data (chi(2)/degree of freedom = 1.6), to predict deeply bound K- atomic levels, not yet detected. This improved potential predicts, in general, states even narrower than those recently reported by Friedman and Gal [9]. This reinforces the idea that these deeply atomic states can be detected and resolved by using suitable nuclear reactions. Besides, we also study K- and (K) over bar(0) nuclear bound states and compute binding energies and widths, for both species of antikaons, in C-12, Ca-40 and Pb-208. Despite of restricting our study only to potentials obtained from best fits to the known kaonic atom data, the dynamics of these nuclear bound states depends dramatically on the particular optical potential used.