  We study degree spectra of structures with respect to the bi-embeddability
relation. The bi-embeddability spectrum of a structure is the family of Turing
degrees of its bi-embeddable copies. To facilitate our study we introduce the
notions of bi-embeddable triviality and basis of a spectrum. Using
bi-embeddable triviality we show that several known families of degrees are
bi-embeddability spectra of structures. We then characterize the
bi-embeddability spectra of linear orderings and study bases of
bi-embeddability spectra of strongly locally finite graphs.
