A tiled map is a map which can be displayed in a browser window. It is made up of many individual image files, which are seamlessly stitched together for easy navigation. The Pelagios Map Tiles are a set of resources that allow you to project data onto dynamic maps dedicated to different historical periods or types of map imagery. These maps are open source and free for use in research, teaching or general interest.
The most detailed map available is the Digital Map of the Roman Empire, created by community member Johan Åhlfeldt at Lund University, Sweden. He created a static (non-layered) map of the ancient places in the Pleiades dataset which has the capacity to serve as a background layer to online mapping applications of the Ancient World. This map was created using the Pleiades gazetteer and the Digital Atlas of Roman and Medieval Civilizations (DARMC), both of which are based on the Barrington Atlas of the Greek and Roman World. This map features details such as major and minor roads, aqueducts, temples, cemeteries and quarries. You can find out more details about the map and how Johan created it here.
You can also use the geographically accurate basemap of the ancient world created by the Ancient World Mapping Centre, University of North Carolina at Chapel Hill.
Historical data can be mapped to modern places and roads using the OpenStreetMap tiles.
Finally, you may want to map your data to current aerial imagery via Mapbox.