Land plants and algae are now represented by about 40 genomes. Although most are incomplete, putative globins appear to be present in all the ca. 30 land plant genomes and in all except one algal genomes. The globins have either the canonical 3/3 α-helical fold characteristic of vertebrate myoglobin (Mb) or 2/2 α-helical folds, characteristic of bacterial globins with a truncated Mb-fold. In view of the fairly complete picture of the globin superfamily that is now available from analyses of over 1,000 bacterial genomes and >200 other eukaryote genomes, it is now possible to seek answers to the following twin questions: what is the phylogenetic relationship of plant and algal globins to those of other eukaryotes and what is their likely bacterial origin? We summarize below the available results. Molecular phylogenetic analyses indicate that plant and algal 3/3 globins are related to bacterial flavohemoglobins and vertebrate neuroglobins. Furthermore, they also suggest that plant and algal 3/3 and group 1 2/2 Hbs originated from the horizontal gene transfers that accompanied the two generally accepted endosymbioses of a proteobacterium and a cyanobacterium with a eukaryote ancestor. In contrast, the origin of the group 2 2/2 Hbs unexpectedly appears to involve horizontal gene transfer from a bacterium ancestral to Chloroflexi, Deinococcales, Bacillli and Actinomycetes. We present additional results which indicate that the shared ancestry is likely to be with the Chloroflexi alone.