Squats really are a runners best friend! In the sports lab where I work, a common answer for people coming in with knee problems and even poor balance is because of poor gluteal strength. The three key muscles are the Gluteus Maximus, Gluteus Medius and Gluteus Minimus. Out of all 3 glute max is the largest. Therefore, big gross movements involving the lower limbs will always activate this muscle: Squats (Sumo/Bulgarian and Standard), Lunges and Deadlifts (also a key hamstring exercise) are essential.
These exercises cant just be performed and think ‘Oh thats simple’. Many clients i see perform a lunge and allow their hips to not stay level. This is in fact showing how weak that gluteal muscle actually is. Therefore, the slower and more controlled these exercises are performed engaging the core at all times, the better. The Deadlift does use more hamstring strength dependant on which version you perform. Above is the Romanian deadlift which uses only a slight bend in the knee. To activate glutes in a greater way, full deadlift (knees bent) will do more.
Now the Gluteus Medius is a muscle key in the roll of stabilisation of the femur and therefore its strength has a great impact on knee stability. The Gluteus Minimus is also utilised in the stability of the femur as it is attached to it! The exercises below performed correctly can help to strengthen and loosen this area. We must not forget the tightness of a muscle means it is not able to function well. So stretches are paramount!
While performing the glute bridge above, glutes must be squeezed at the top to add to the quality of the movement. On the right is an advancement once the core is strong enough to hold the position.
Two stretches above are my favourite loosening off exercise for the glutes. Others can include using a medicine ball or tennis ball to sit on a roll around the affected area also. Once found just sitting and putting pressure through the point of tightness can help to release the muscles!
Now obviously you have far more muscles inter-twined within the hips and the lower region of the back (erector spinae, piriformis, tfl etc.), so doing exercises to help strengthen and stretch these gluteal muscles will have a knock on effect to smaller muscle groups. There are also sooooo many more exercises you can do to strengthen this area like single leg squats, single leg balance work and bounding. By doing some of these regularly will make you a far more efficient and stronger runner!
(all images obtained from http://workoutlabs.com/exercise-guide)