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.
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