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Please note: The list was updated May 2019, based on a project to summarize the current genera in the Glomeromycota and on new genera published. There is many genera published recently, some without need and unfortunaltely forcing splits into more and more monospecific and/or problematic genera. The community has to make up its own opinion, and may wonder about some editors and their policies.
We do not adopt the recently suggested systematics placing of AMF in the "Glomeromycotina". To our opinion the phylum level will eventually be resurrected, thus we stay with it. As names above the rank of family are not governed by priority in the Botanical Code, you are free to use whichever name you prefer, above family rank.
There were a number of questionable taxa published, but not for all of them formal action was taken (for discussions see, e.g., Redecker D, Schüßler A, Stockinger H, Stürmer SL, Morton JB, Walker C (2013) An evidence-based consensus for the classification of arbuscular mycorrhizal fungi (Glomeromycota). Mycorrhiza 23: 515-531 [doi: 10.1007/s00572-013-0486-y]; Schüßler A, Walker C (2010) The Glomeromycota. A species list with new families and new genera. A. Schüßler & C. Walker, Gloucester [full text PDF]; Morton JB, Msiska Z (2010) Phylogenies from genetic and morphological characters do not support a revision of Gigasporaceae (Glomeromycota) into four families and five genera. Mycorrhiza 20:483-496 [doi: 10.1007/s00572-010-0303-9].Bills and Morton 2015, Redecker et al. 2013, Schüßler and Walker 2010). We indicate some problems, below.