I'm surprised this term shows up much anymore. Though it's a part of history now, the following paper by Woese demonstrated the three domain system long ago.
This, however, is the net result of the sequenced genomes of eukaryotes, archaea and bacteria:
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Source: Toward automatic reconstruction of a highly resolved tree of life.
The phylogenetic differences between these organisms shed light that bacteria and archaebacteria were not as closely related as was initially though, hence the abolishment of Monera.