In this contribution we report on theoretical studies of $\eta$ nuclear quasi-bound states in few- and many-body systems performed recently by the Jerusalem-Prague Collaboration [1-5].
Underlying energy-dependent $\eta N$ interactions are derived from coupled-channel models that incorporate the $N^*(1535)$ resonance. The role of self-consistent treatment of the strong energy dependence of subthreshold $\eta N$ amplitudes is discussed.
Quite large downward energy shift together with rapid decrease of the $\eta N$ amplitudes below threshold result in relatively small binding energies and widths of the calculated $\eta$ nuclear bound states.
We argue that the subthreshold behavior of $\eta N$ scattering amplitudes is crucial to conclude whether $\eta$ nuclear states exist, in which nuclei the $\eta$ meson could be bound and if the corresponding widths are small enough to allow detection of these $\eta$ nuclear states in experiment.