My background is in traditional folk music, and modes are the bread and butter of that type of music. Most British folk songs are in the Dorian/Aeolian modes or the Mixolydian mode. I say Dorian/Aeolian because a weird thing I've noticed is that a lot of traditional melodies don't use the sixth degree of the scale which would differentiate between the two, so it's not always obvious. I've often wondered if modes came instinctively to our ancestors, because the vast majority of people who came up with these songs would have had no musical education whatsoever, and were simply playing and singing the notes which felt right to them.
I originally learned the modes in terms of playing the white keys on a piano starting on different notes, which makes a lot of sense if you're a piano player (as I used to be!) but not much help at learning to apply the modes in practice or understand how they're constructed. So more recently I have been thinking more in terms of 'a major scale with a flattened 3rd and 7th' etc, and that's been much more helpful.
That said, I'm not very technically minded as a musician and thinking about scales too much makes my brain hurt, so I usually work with the modes in a more intuitive way. They each have their own character or emotional mood, which can be very powerful to experience. What works especially well with folk music is to use a drone (root or root and fifth) and then explore how the melody creates a harmony against it. The different modes do this in such a different way it is fascinating to experience their different characters.
I love modes, even though I'm still a long way off properly understanding them!