For those of us in New Testament studies, anything east of Galatia is bit of a mystery. But you only have to read Horace and Revelation to know the seriousness of the threat that Parthia served to Roman clients in the east. The Euphrates was a de facto border between the two empires and it was not until the campaigns of Trajan 116-17 CE that Rome was able to subdue Parthia. For some useful maps of the Parthinian empire see these which include Parthia at the height of its powers. Essentially the Parthinian empire took over from the shrinking Seleucid empire and soon controlled modern Iran, Iraq, Armenia and parts of Turkey and Afghanistan.
For another good map of the Roman empire see this one which is searchable.