Exercises for the thigh muscles usually target more then one particular muscle group.
Remember, during these exercises, always breathe evenly using your diaphragm but not your upper chest.

Rectus Femoris is a superficial muscle located on the front of your thighs. Iliopsoas are the deep muscles located to the sides and slightly above of the pubic area.
Exercises for the core strength are good exercises for the hip flexors. When you stretch the hamstrings, you should learn to engage your hip flexors for better results. For an explanation, see Hip Flexibility.

• Reversed Sit-up - Sit on the floor, legs together, and bend your knees. Either stabilize your feet under a sofa, or ask someone to hold them. Sit close to your legs, back straight and arms folded in front. Create an abdominal push, exhale and slowly lower your torso (from the hips) down just a little bit, 5-15 degrees. Bring it back on the inhale. Keep your back straight all the time.

  	Do not arch your lower back. If you only lower your upper body you have failed to create the abdominal push.

  Repeat 10 times and do 2-3 series. Lowering your body further is less important than doing more repetitions. Women can do this exercise without stabilizing their feet, because their lower body is heavier then upper body. This exercise is working the iliopsoas very hard.
• Clock Exercise - Kneel on the floor/mat. Keep your body upright with the trunk and thighs in a vertical line. Either put your arms by your side, or fold them in front of you or behind your head. Create an abdominal push and lean backwards from your knees a few degrees. You should not arch your back. Your body, from the head to the knees, should form a straight line at all times. Come back to the vertical position. To create more work for the rectus femoris muscle make sure you do not engage your buttocks.
  Move slowly and in control. Lean backwards only as far as you can handle comfortably. Repeat 10 times and do 2-3 series, resting in between.

  	If you feel discomfort or pain in your neck, back or knees consult your physician before continuing with the exercise.

• Rider's Posture - Stand sideways to the tall mirror and in front of a wall or a solid piece of furniture. Put your feet parallel to each other and at the shoulder width. Now, look into the mirror, keep your body vertical and bend your knees. Your knees must go down and forward and come in contact with the wall in front of you. Put some weight into that contact. Look in the mirror. You will see yourself in the posture of a rider. Note that your pelvis is in a neutral position and you can draw a vertical line through your ear, shoulder, hip and heel. Still watching yourself in the mirror, keep your knees against the wall, your torso vertical, and move your body down and backwards by slightly bending your knees. Come back up and forward with your body. This exercise mainly works the rectus femoris muscle.
  Repeat 10-15 times and do 2-3 series, resting in between. At first, move slowly and in control. When you get better, increase the speed without losing the control.

  	If you feel any discomfort or pain in the knees consult your physician before continuing with the exercise.

• Modified Bridge (using your upper thighs) - Lay on your back, bend your knees, and put your feet slightly apart. Push your feet down and start unbending your knees. This will lift your thighs into the air and your body will follow. Do not engage your buttocks. Keep your body and thighs in line, and do not arch your back.
  First variant: Lift and lower your hips. Repeat 10 times and do 2-3 series, resting in between.
  Second variant: Hold the hips lifted as long as you can, building up to 30 seconds. Repeat a few times, resting in between.

To combine a workout for hip extensors and upper thighs, use the previous exercise - Modified Bridge. In that position you can use two different methods to lift your hips. You can either engage your upper thighs, or you can use your buttocks and hamstrings.
First variant: Move your hips up and down alternating these methods.
Second variant: Hold the hips lifted and switch between these two muscles groups without lowering your hips.

Click here for exercises on abductors, adductors and thigh rotators.