The Romans arrived in modern-day Germany as part of a larger military campaign.  They were led by the famous general and the leader of Rome, Julius Caesar.   In approximately 50 BC, Caesar arrived with his legions (army).  Over the several hundred years they established the northern edge of the Roman empire.  The border that eventually was created between the Roman territory and the Germanic tribal lands was referred to as the Limes Germanicus (German frontier).   The border ran roughly along the lines of both the upper Danube River and the Rhine River.  
The Germanic tribes proved themselves to be powerful and tenacious warriors.  This made it both costly and almost impossible to extend the Limes Germanicus.  In the famous Battle of Teutoburg Forest in the fall of AD 9, the Romans generals were defeated by the Germanic tribe leader Arminius.  The Romans lost several legions, over 15,000 soldiers, making it one their deadliest defeats.   
The result of Roman's encounters with the Germanic tribes was that they built of series of fortresses along the Limes Germanicus.   The ruins of those forts as well as other relics from the Roman era can still be seen today.