I carry a Garmin 62S with an Open Streets map layer that I download off the internet, cycling layer. That usually tells me a lot about other roads around detours, etc.
But the Garmin screen is small, so when I need more screen room for planning, I use an Android based 7 inch tablet. I have two pertinent apps, Maps.Me (free) (formerly named Maps With Me) and Soviet Military Maps Pro ($11) with Open Streets Cycle layer. I load the maps for where I will be on the internet before I leave home on both apps. Those three options are usually all I need.
While I also like street maps on paper, simple fact is that when you are biking hundreds of miles it can be impractical to find and carry the street maps you might need for small towns or rural farm areas. I however have e-mailed other states where I plan to travel and ask them to mail me state highway maps or other pertinent maps, those can be a big help.
Also carry a compass, but I do not recall the last time I actually used it.