The genus was circumscribed by the Finnish lichenologist William Nylander in 1875. Nylander erected Magmopsis to accommodate a small, sooty-grey crustose lichen, Magmopsis pertenella. This lichen had immersed, black apothecia that he described as "pyrenio-type conceptacles" (perithecioid ascomata). In sectioning he found the interior of the fruiting bodies white, and noted eight hyaline, ovoid, 1-septate ascospores, measuring about 14–16 μm × 6–7 μm; the paraphyses were slender and sparse to evanescent. The hymenial gel did not stain with iodine (I−), and the ascus contents appeared wine-brown in iodine. The apothecia were tiny (about 0.13–0.14 mm across). Nylander's material came from calcareous rock in the Ladoga region of Finland, collected by Johan Petter Norrlin.[3]
In discussing placement, Nylander treated Magmopsis as allied to the "Phylliscodeae" (his usage) or even warranting a tribe of its own. He remarked that the apothecia seemed peridiate and he could not find a true ostiole, drawing an analogy to Mycoporum within the byssoid lichens of his time. Nevertheless, he considered the taxon difficult to assign to the pyrenocarpous tribes sensu the nineteenth-century systems and kept it with apothecioid lichens rather than among true pyrenocarps.[3]
A second species, Magmopsis argilospila, was added to the genus by Nylander in an 1886 publication of James Crombie's.[4]
In 2013 Kevin Hyde and colleagues, in their work on Dothideomycetes classification, wrote "Magmopsis Nyl. appears to be a synonym of Pyrenopsis in Lichinaceae".[5] As of 2016, there was no molecular data available for Magmopsis.[6]