What precisely are E∞ring spaces and E∞ring spectra?

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Units of ring spectra and Thom spectra (2008, background): “d to an E∞ ring spectrum R.Motivated by the adjunction (1.6), or more precisely its restriction to abelian groups Z: (abelian groups) //(commutative rings) : GL oo 1, we prove the following (see also [May08]). Theorem 2.1 (Theorem 3.2). The functor gl1 participates as the right adjoint in an adjunct”
More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, background): “2It is part of the 1970’s story of infinite loop space theory and E∞ ring spectra; see [86] for a 1970’s overview and [92] for a modernized perspective.”
Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory (2014, unknown): “uivalence gives rise to a weak equivalence of C-spaces |ΩfΣfB •(C∗,C∗,X)| → Ω f|ΣfB •(C∗,C∗,X)| ∼= ΩfΣfB(C∗,C∗,X) 38 ANDO, BLUMBERG, GEPNER, HOPKINS, AND REZK by passage to colimits. (We note that in [27], May describes proving that (5.49) is a weak equivalence as the hardest thing in [24].) Therefo”
Models of G–spectra as presheaves of spectra (2011, background): “It is impossible to have both of these conditions in the same symmetric monoidal model category for the stable homotopy category [L,M7].”
Equivariant iterated loop space theory and permutative G–categories (2012, unknown): “Pragmatically, use of the two-sided bar construction as in [23, 31] gives all that is needed.”