The actual gluteal muscle does not often, in itself, become strained. Usually, only something like deep squatting causes it.
However, there are several deep muscles in the back of the hip, deep to the gluteal muscle, that cause problems. The deep hip rotators are in close proximity to the sciatic nerve as it passes through and can become tight as a consequence of irritation in the back – a byproduct of sciatica. Further, they can become spasmed with sacroiliac joint issues. (Pelvis), and piriformis syndrome.
There is much that can be done for this – essentially by treating the cause which is the back and pelvis, as well as treating the deep muscle tightness with mobilisation and exercise as well as acupuncture on occasion.
The gluteal tendon can become thick and fibrosed with lots of squatting and running type activities. This can be very uncomfortable to sit on and to walk and run. Treatment involves a lot of deep mobilisation work, shockwave and exercise to treat the tendon. They are often confused with high hamstring tendinopathy and sometimes go hand in hand.