The Roman Empire did not simply disappear overnight. A slow and steady decline in culture and wholeness eventually caused the collapse of this once great empire. The Greek portion, the Byzantine Empire with its capital in Constantinople was kept strong for much longer by the efforts of Basil II and the Komnenus. But still, this eastern portion eventually collapsed as well.
After the fall of these great empires, their influences are still evident. Central-planned churches kept up popularity for a long time, and almost all mosques begin to be built this way. Onion-shaped domes are simply evolved domes and they can be found throughout history. Renaissance architecture also utilizes the new dome style, and in Greece this carries on today. The predecessor of the dome, the arch, is obviously still used today. The basilica structure was also heavily used, and it in turn inspired other styles after that. Roads, and the techniques to build them have influenced modern infrastructure and modern amphitheaters are obviously direct nods to the Ancient Roman ones.