Mondasian Cybermen are Cybermen that hail from the planet Mondas. Unlike their Parallel Counterparts, they were created in our universe and are noticably weaker. However, they were still powerful enough to subjugate many lesser races and convert them to 'Cyberform'.
They scoured the Galaxy upgrading people, but they were stopped in several places by superior forces. Initially, the League saw the Cybermen as a threat, and outcasted them. However, there were very few engagements between the Cybermen and the League.
The Cybermen also attacked many planets, like Telos Minor and Earth, but one of their main problems was the sheer idiocy of their leader, the Cyberleader. Driven mad with power, each and every Cyberleader had a massive god complex and their ludicrous plans very nearly wiped out the Cybermen several times.
They were brought to the brink of extinction during the Cyberman-Borg War, and what is left of them has joined with the Cyberman Remnant to form a combined race of Cybermen.
They are recognised as a mighty race after their war with the Borg, since they provided the Galaxy with a cure for Borg Assimilation. The Cybermen as a whole were much more appreciated after this, and they didn't fail as much because they did not have Cyberleader telling them what to do.