Borders of the Roman Empire
The borders of the Roman Empire, which fluctuated throughout the empire's history, were a combination of natural frontiers (most notably the Rhine and Danube rivers) and man-made fortifications which separated the lands of the empire from the "barbarian" countries beyond.
A limes was a border fortification system of the Roman Empire. The Latin noun "limes" had a number of different meanings: a path or balk marking off the boundaries of fields; a boundary line or marker; any road or path; any channel, such as a stream channel; or any distinction or difference between two things. Hence it was utilized by Latin writers to denote marked or fortified frontiers. The name given to proper Walls was vallum, which might have represented a border. In Britannia the Empire built two walls one behind the other, for Mauretania there was a single wall with forts on both sides of it. In other places, such as Syria and Arabia Petraea, there wasn't a continuous wall; instead there was a net of border settlements and forts occupied by the Roman army. In Dacia, the limes between the Black Sea and the Danube were a mix of the latter and the wall defenses: the Limes Moesiae was the conjunction of two, and sometimes three, lines of vallum, with a Great Camp and many minor camps spread through the fortifications.
So far the traditional use of the term. It is now more common to accept that this is an anachronistic terminology, reflecting the views of modern scholars more than Roman reality. Limes was in fact not used to indicate the imperial frontier or a fortified border. After the third century it was an administrative term, indicating a military district, commanded by a dux limitis.
The northern borders
In continental Europe, the borders were generally well defined, usually following the courses of major rivers such as the Rhine and the Danube. Nevertheless, those were not always the final border lines; the province of Dacia, modern Romania, was completely on the far side of the Danube, and the province of Germania Magna, which must not be confused with Germania Inferior and Germania Superior, was the land between the Rhine, the Danube and the Elbe (Although this province was lost three years after its creation as a result of the Battle of Teutoburg Forest).
In Great Britain both Hadrian and Antoninus Pius built defences to protect the province of Britannia from the Caledonians. Hadrian's Wall, constructed in 122 held a garrison of 10,000 soldiers, while the Antonine Wall, constructed between 142 and 144, was abandoned by 164 and briefly reoccupied in 208.
The Pannonian Limes
The eastern borders
The eastern borders changed many times, of which the longest lasting was the Euphrates river, eventually to be left behind as the Romans defeated their rivals, the Parthians, with the march on their capital, Susa in 115. The Parthians were a group of Iranian peoples that ruled most of Greater Iran that is in modern-day Iran, western Iraq, Armenia and the Caucasus. In 118 Hadrian decided that it was in Rome's interest to re-establish the Euphrates as the limit of its direct control. Hadrian returned to the status quo ante, and surrendered the territories of Armenia, Mesopotamia, and Adiabene to their previous rulers and client-kings and didn't attempt to romanize the Parthian Empire. 
The southern borders
At the greatest extent of the Empire, the southern border lay along the deserts of Arabia in the Middle East and the Sahara in North Africa, which represented a natural barrier against expansion.
The Empire controlled the Mediterranean shores and the mountain ranges further inland. The Romans attempted twice to occupy the Siwa Oasis and finally used Siwa as a place of banishment.
However Romans controlled the Nile many miles into Africa up to the modern border between Egypt and Sudan.
Septimius Severus expanded the "Limes Tripolitanus" dramatically, even briefly holding a military presence in the Garamantian capital Garama in 203 AD. Much of the initial campaigning success was achieved by the legate of Legio III Augusta, Quintus Anicius Faustus.
- Benjamin Isaac, The Meaning of "Limes" and "Limitanei" in Ancient Sources, Journal of Roman Studies 78(1988), 125-147
- Benjamin Isaac, The Limits of Empire: the Roman Army in the East (Oxford University Press, revised ed. 1992)
- Map of Roman Africa
- De Agostini (2005). Atlante Storico De Agostini. Novara: Istituto Geografico De Agostini. ISBN 88-511-0846-3.
- Camer, Augusto and Renato Fabietti. Corso di storia antica e medievale 1 (seconda edizione). ISBN 88-08-24230-7.
- Grant, Michael (1994). Atlas of Classical History (5th edition). New York: Oxford Univ. Press. ISBN 0-19-521074-3.
- Scarre, Chris (1995). The Penguin Historical Atlas of Ancient Rome. London: Penguin. ISBN 0-14-051329-9.