The Romans did not invent the arch, but previous cultures had made little use of it and certainly did not spot its potential. The Romans did. Arches were made narrower and pillars made bigger the higher the arch, up to c. 20m; if more height was necessary, they built two tiers, with the pillars of the second tier resting on those of lower – lower arches then act like braces to support the pillars. Shaped arch stones are called voussoirs; more shaped stones are placed above them to create level surface across the arch. Arches in sequence (making a continuous ‘tube’, called a barrel vault) create a space that could go on and on. Barrel vaults set at right-angles to one another create groin-vaults with which a large rectangular space could be roofed from relatively few pillars, as in e.g. the Piscina mirabile illustrated here
Vaults were sometimes set in circle or ellipse, as in e.g. the Flavian amphitheatre at Puteoli, illustrated here. The lower arches create cubicles for animal cages; a second tier is set back on the floor above. The cages could be moved forward and lifted up to the arena floor (where the animals might appear to emerge from caves or similar naturalistic scenery constructed there) through the holes in the roof of this substructure.
The arch was also used in an arched dam; see here.