**Abstract**

High-Tc superconductors (SCs) are most widely studied via the multiband approach (MBA) based on the work of Suhl et al. and the Nambu-Eliashberg-McMillan extension of the BCS theory. Complementing MBA and presented in a recent monograph is an approach based on the generalized BCS equations (GBCSEs), which too has been applied to a significant number of SCs. GBCSEs are obtained via a Bethe-Salpeter equation and the Matsubara technique. One of the key features of this approach is the characterization of a composite SC by Cooper pairs with different binding energies—each of which is identified with a gap (Δ) of the SC—depending on whether pairing is due to phonon exchanges with one, two, or more ion species. Another feature is the incorporation of chemical potential in the GBCSEs, which enables one to calculate the critical current density j0 of an SC using the same parameters that determine its Tc and Δ. Following a review of the concepts of this approach, given herein, for the first time, is a detailed explanation of the multitude of reported empirical values of {Tc, Δ, j0} of Bi2Sr2CaCu2O8. Also discussed are the currently topical issues of s-superconductivity and the isotopelike effect for high-Tc SCs.

**Keywords:** high-Tc superconductors, multiband approach, GBCSE-based approach, superconducting features of Bi2Sr2CaCu2O8, s-superconductivity, isotope-like effect for high-Tc superconductors, suggestions for further increasing the Tc of the Bi-based superconductors
