When we heard about airways, we usually talk about VOR airways or Tango airways (Navigational Routes). However, before the days of VOR airways, airways are used to be defined by NDBs and they still do exist! Though they are dwindling in numbers and certainly are dying as NDBs are being decommissioned.
The colored airways are identified by their colors (Amber, Blue, Green, or Red) and a number. Green/Red ones are West/East bound and the other two are North/South bound. Take the Nome sectional chart in Alaska for example, you can see the R-35 and G-212 airways defined by the Fort Davis NDB.
Today they really only exists in Alaska (and somehow… in Canada but in FAA orders?) and only 11 of them still do exists. You can find all of them in FAA Order JO 7400.11K.