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abstract: 'We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. Specifically, we show that for an ${E_{\infty}}$ ring spectrum $A$, the classical construction of ${{gl_{1}}A}$, the spectrum of units, is the right adjoint of the functor $${{\Sigma^{\infty}}_{+}}{\Omega^{\infty}}: \operatorname{ho}{(\mbox{connective spectra})} \rightarrow \operatorname{ho}{(\mbox{${E_{\infty}}$ ring spectra})}.$$ To a map of spectra $$f: b \to b{{gl_{1}}A},$$ we associate an ${E_{\infty}}$ $A$-algebra Thom spectrum $Mf$, which admits an ${E_{\infty}}$ $A$-algebra map to $R$ if and only if the composition $$b \to b{{gl_{1}}A} \to b{{gl_{1}}R}$$ is null; the classical case developed by [@MQRT:ersers] arises when $A$ is the sphere spectrum. We develop the analogous theory for ${A_{\infty}}$ ring spectra. If $A$ is an ${A_{\infty}}$ ring spectrum, then to a map of spaces $$f: B \to B{{GL_{1}}A}$$ we associate an $A$-module Thom spectrum $Mf,$ which admits an $R$-orientation if and only if $$B \to B{{GL_{1}}A} \to B{{GL_{1}}R}$$ is null. We note that $B{{GL_{1}}A}$ classifies the twists of $A$-theory. We take two different approaches to the ${A_{\infty}}$ theory which are of independent interest. The first involves a rigidified model of ${A_{\infty}}$ (and ${E_{\infty}}$) spaces, as developed in [@Blumberg-thesis; @Blumberg-Cohen-Schlichtkrull]. The second uses the theory of $\infty$-categories as described in [@math.CT/0608040] 