  Eta-mesic nucleus or the quasibound nuclear state of an eta ($\eta$) meson in
a nucleus is caused by strong-interaction force alone. This new type of nuclear
species, which extends the landscape of nuclear physics, has been extensively
studied since its prediction in 1986. In this paper, we review and analyze in
great detail the models of the fundamental $\eta$--nucleon interaction leading
to the formation of an $\eta$--mesic nucleus, the methods used in calculating
the properties of a bound $\eta$, and the approaches employed in the
interpretation of the pertinent experimental data. In view of the successful
observation of the $\eta$--mesic nucleus $^{25}$Mg$_{\eta}$ and other promising
experimental results, future direction in searching for more $\eta$--mesic
nuclei is suggested.
