A consistent and unified microscopic theory of superfluidity and superconductivity is developed on the basis of two-stage Fermi-Bose-liquid (FBL) (in particular case, one-stage Bose-liquid) scenarios. It is shown that these phase transition scenarios is accompanied, as a rule, by the formation of composite bosons (Cooper pair and bipolarons) with their subsequent single particle (SPC) and pair condensation (PC). A brief outline of the modified and generalized BCS-like pairing theory of fermions is presented. In an analogy to that, a detailed boson pairing theory is developed. The SPC and PC features of an attracting 3d- and 2d-BG as a function of the interboson coupling constant in the complete range 0≤T≤T_B is studied in detail. It is argued that the coexistence of the order parameters of attracting fermions Δ_F and bosons Δ_B leads to the superfluidity (in³He) and superconductivity (in superconductors) by two FBL scenarios. One of these scenarios is realized in the so-called fermion superconductors (FSC) and the other in the boson superconductors (BSC) in which the gapless superconductivity is caused by the absence of the gap Δ_SF in the excitation spectrum of bosons and not by the presence of point or line nodes of the BCS-like gap Δ_F. The new adequate definitions for basic superconducting parameters of FSC and BSC are given. The theory proposed is consistent with the experimental data available.

So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like ($s-$ or $d-$wave) pairing theory is adequate for explaining high-$T_{c}$ superconductivity in doped cuprates from underdoped to overdoped regime.We show that the doped cuprates, depending on the Fermi energy ($\varepsilon_{F}$) and the energy ($\varepsilon_{A}$) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $\varepsilon_{A}/\varepsilon_{F}$ and $\Delta/\varepsilon_{F}$ (where $\Delta$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high-$T_{c}$ superconductivity is quite different from the BCS-type ($s-$ or $d-$wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ($T_{c}$) and the peculiar oxygen and copper isotope effects on $T_{c}$ in overdoped cuprates.