Mixolydian forms the third part of the holy triumvirate of the ii V I progression, which makes it important enough, but add to it that it also can be the basis for the blues, and any other dominant 7 chord, and it becomes one of the most important modes in your scale arsenal.
Mixolydian is a major scale with a b7; so C mixolydian is spelled: C D E F G A Bb C, and it goes with a C7 chord. Again, you can use three different major pentatonic scales to create the sound of C mixolydian. The first choice is C major pent, which is C D E G A. It doesn’t get the mixolydian note of Bb, but it’s very straightforward and tuneful, and it works great for blues, which most of you who are reading this already know. The second, less obvious choice is F major pent: F G A C D. The F is a tension note, and must be treated as such. The third choice, which gets the “mixolydian note” is Bb major pent: Bb D C F G. This scale is fun to try, because it makes the sound of mixolydian in a more outside way. It gives you a suspended, jazzy kind of sound. Think mixolydian from Mars.
To transpose, think of mixolydian with major pent as: I/I (one over one or C over C in the example), IV/I (four over one or F over C in the example), and bVII/I (flat seven over one or Bb over C in the example). Play around with using all three over a static chord to find the tension and release of the three scales.
An example over an Bb7 chord would be: Bb major pent, Eb major pent, and Ab major pent. Enjoy!