Obviously much of this appears in fantasy (like in GoT or fantastical depictions of Ancient Rome), but it comes up so often I have begun to wonder. Thanks!
Short answer:
To the extent that the Romans had maps, they were a bit like the "map" in the title credits of Game of Thrones. Evocative, with regional and historical themes illustrated, but not of practical use. Military leaders seem to have planned verbally, with reference to tables of distances, but not by moving pieces on maps. We've got lots of Roman military artifacts, but no hint of "pieces" to represent legions.
Discussion:
The Romans, interestingly, seem not to have had maps in the sense we mean them, for military or navigational use. They did produce itineraries, essentially linked nodes-- "first you go here, then you go through the pass, then its 20 miles to the river"; but true cartography is missing. These itineraries look more like the "map" of the NYC subway or the London Underground. We don't have surveys of terrain, just distances between places with connections and obstacles listed.
Vegetius is the most explicit source:
[The commander] should have itineraries of all regions in which war is being waged written out in the fullest detail, so that he may learn the distances between places in terms of the number of miles and the quality of roads, and examine short-cuts, by-ways, mountains and rivers, accurately described.
Elsewhere he suggests that some of these places might be "illustrated", but there's no real connotation of a map. We have a surviving example of one of these military itineraries for practical use, inscribed on a Roman soldier's shield, the "Dura-Europos Route Map". It's basically like a trail map, or a sailor's periplus-- a list of distances and towns along the way. The famous Peutinger Table is a very grand example of this.
There is mention of great displays of the Empire and world, like Agrippa's Orbis Terrarum, but no suggestion that these had any practical use. Pomponius Mela created a kind of world map, but we have no indication that military utility was an aim. There _is_ a reference to Caesar commissioning a map from Greek geographers, but no indication if it ever was completed, nor reference to anything like that in use. Ronald Syme characterizes their purpose: "Maps of countries came mainly on show for decorative purposes, being paraded in triumphal processions; and the Temple of Tellus exhibited a picture of Italy".
Reading Caesar, you get lots of discussion of tactical disposition, but so far as one can tell, his understanding of the military situation is entirely verbal. He will frequently refer to being informed about the enemy's disposition by a scout or some friendly (or coerced) local.
Here's a typical description from the Gallic Wars
After [Caesar] had made three days march through their territories, he discovered from some prisoners, that the river Sambre was not more than ten miles from his camp; that all the Nervii had stationed themselves on the other side of that river, and together with the Atrebates and the Veromandui, their neighbors, were there awaiting the arrival of the Romans
So he seems not to have known about a river ten miles away . . . taking him at his own word, and Caesar isn't inclined to diminish his own perspicacity, what he knew of the enemy disposition and the local terrain he learned by word of mouth from prisoners.
Elsewhere he often refers to his scouts and skirmishers and local allies giving important information about local terrain and the enemy's location, and that seems to have been the general Roman practice. Famously Varus met his disaster in the Teutoburgerwald when he followed his erstwhile German ally Arminius' suggestion of a shortcut through the woods . . . where the Romans were ambushed and suffered their worst defeat. He had little idea where he was going, nor where his enemies were beyond what his allies told him, apparently.
Sources
The Nature and Genesis of the Peutinger Map
Observations sur l'original du fragment de carte du pseudo-bouclier de Doura-Europos