The Fermi-LAT experiment recently reported high precision measurements of the spectrum of cosmic-ray electrons-plus-positrons (CRE) between 20 GeV and 1 TeV. The spectrum shows no prominent spectral features, and is significantly harder than that inferred from several previous experiments. Here we discuss several interpretations of the Fermi results based either on a single large scale Galactic CRE component or by invoking additional electron–positron primary sources, e.g. nearby pulsars or particle dark matter annihilation. We show that while the reported Fermi-LAT data alone can be interpreted in terms of a single component scenario, when combined with other complementary experimental results, specifically the CRE spectrum measured by H.E.S.S. and especially the positron fraction reported by PAMELA between 1 and 100 GeV, that class of models fails to provide a consistent interpretation. Rather, we find that several combinations of parameters, involving both the pulsar and dark matter scenarios, allow a consistent description of those results. We also briefly discuss the possibility of discriminating between the pulsar and dark matter interpretations by looking for a possible anisotropy in the CRE flux.