It is important to focus on the gluteus maximus as a fitness competitor for many reasons. One being most judges will determine how conditioned you are by the tightness and shapeliness of the lower half as it is one if the hardest part to tone and lean for most females genetically.

Whether it is for a competition or looking and feeling good in your jeans,  for the most part women want a nice shapely back side. 

First of all the glutes are made up of three parts. The Gluteus medius, minimus and maximus. The maximus makes up the large part of the the appearance of the buttocks. It is responsible for maintaining the trunk in an upright position.

What to remember while training gluteus maximus.

Form and technique while doing deep squatting. With good form deep squatting will activate and strengthens your glutes and lower back much more then parallel squats.  For deep squatting you should point toes slightly outwards and stand in a wide stance so it allows for more space for hip flexion at the bottom.   Make sure you stretch and don’t be afraid to hit the squat rack. 

Lift heavy. Your glutes are the largest muscle group in your body. So you should train them like any other muscle group. Instead of doing your reps high and light, isolate those glutes with heavy weight on a stable surface area. One good example is barbell Glute bridges. 

Train them often as part of your weekly routine. If you really want to improve that area you might have to incorporate them 2-3 times a week. If you are going heavy a couple of good exercises each day would be efficient. 

Good carbohydrates are your friend when it comes to tight glutes. If you don't eat enough carbohydrates your glutes will look flat and soft.

Don't do too much cardio. Sometimes if you over do it, your muscle fibers do not gain muscle but actually do the opposite and to be more made endurance training resulting in more of the "rail like physique" then a definition of a let’s say a “sprinter”.

15 great glute exercises to incorporate into your weekly routine

I recommend incorporating a couple of these into your workouts 2-3 times a week.

•  Bridge. 
•  Barbell hip thrusts.
• Ham extension lunge with lean forward – the glutes are engaged that way by lengthening the muscle.  
• Step up.  
• One leg box squats. 
• Doggies.  
• Lunge jump.
• Knee through reverse lunges. 
• Straight leg dead lifts.  
• Pretzel side kicks. 
• Box step squat with a lunge and wide step out squat.
• Bridge with leg extension. 
• Butt lifts with TRX bands. 
• Single leg RDL circuit.  Pully variations low med and high. 
• Single leg squats getting up from low bench.