-We report a microscopic model wherein the unconventional superconductivity emerges from an incoherent 'Cooper-pair glass' state. Driven by the pair-pair interaction, a new type of quasi-Bose phase transition is at work. The interaction leads to the unconventional coupling of the quasiparticles to excited pair states, or 'super-quasiparticles', with a non-retarded energydependent gap. The model describes quantitatively the quasiparticle excitation spectra of both cuprates and pnictides, including the universal 'peak-dip-hump' signatures, and for the pseudogap phase above Tc. The results show that instantaneous pair-pair interactions account for the SC condensation without a collective mode.Despite its wide applications, the BCS theory [1] fails to account for the physical properties of a large variety of high-T c superconductors (SC), the cuprate family, but also the more recent iron-based superconductors. A striking feature of these materials is the proximity to an insulating phase, whether anti-ferromagnetic (cuprates), spin density wave (iron based SC, Bechgard salts) or localization (ultra-thin films). Just beyond the insulating phase, the SC dome appears in the phase diagram as a function of carrier concentration between two critical points. Understanding the transition from such an insulating to SC state is still a major challenge.Microscopic measurements reveal an unconventional quasiparticle (QP) dispersion, the 'peak-dip-hump' structure [2], often attributed to the coupling to a collective mode [3][4][5][6][7][8]. Although the peak to dip energy follows both the neutron resonance and T c as a function of doping [6,9,10], the finer shape of the QP spectra and their temperature dependence remain a challenge. Moreover, in the temperature range [T c , T * ] a pseudogap (PG) state persists, having a Fermi-level gap ∆ p much larger than the critical energy scale k B T c in cuprates (see [11] and ref. therein) and also in iron-based SC [12][13][14].In this letter, these questions are addressed within the pair-pair interaction model (PPI). We show that the main unconventional features of high-T c SC can be understood p-1 arXiv:1612.02268v2 [cond-mat.supr-con]