The hip flexors can be used to bend the hip forwards or they can be used to resist the hip bending backwards.
Standing on one leg, the hip flexors can be used to lift the knee of the free leg.
Sitting and balancing on the butt the hip flexors can be used to lift one or both knees.
Sitting with one or both legs straight (or bent) the hip flexors can be used to deepen the forward bend by tilting the pelvis forwards relative to the legs.
In a lunge or front to back splits the hip flexors of the back leg can be used to keep the pelvis from sinking down, or can be used to control the descent of the pelvis.
Doing a straight leg sit up the hip flexors can be used to help tilt the torso upright.
Hip flexors that cross the hip and knee include the rectus femoris, the tensor fascae latae and the sartorius muscle. These latter two muscles may be used as hip flexors is the knee is straight and stabilized.
The quadriceps may be more effective at flexing the hip if the knee is bent or if the leg is flexed from an extended position.
The hip flexor that works on both the hip and the lumbar spine is the psoas major muscle. This muscle bends around the front of the pelvis and so not only can it bend the hip forwards, it also, when the hip is relatively straight, acts to create a rearwards push on the pelvis.
If the hip is bent forwards the psoas major is slackened and it's bend around the pelvis is reduced or completed removed. In this case, to add tension to some fibers of the psoas, the lumbar spine can reverse curvature from a backward bend to a forward bend.
This can be important for creating lumbar stability.
If the lumbar spine isn't reverse curved then with the hips bent forwards, lumbar stability may be created by the transverse abdominus acting in concert with the quadratus lumborum, sacral multifidus and serratus posterior inferior.
The major single joint hip flexor is the iliacus. This connects to almost half the inner surface of the pelvis. It to folds around the front of the pelvis along with the psoas major and along with it connects to a point near the top of the inner thigh, just below the neck of the femur, called the lesser trochanter.
The pectineus connects from the front of the pelvis, near the pubic bone, the lesser trochanter. It has a similiar line of pull to the psoas and iliacus, but along a shorter distance.
The obturator externus may also be used to help flex the hip. It attaches to the pelvis below the hip socket, covering part of the opening at the side of the pelvis below the hip (the obturator foramen.) It passes below the neck of the thigh bone, then reaches up behind it to attach to the inner surface of the greater trochanter.
At the very least, in a forward bend for the hips, where the psoas ceases to bend around the front of the pelvis, and thus can no longer create a backwards push on the pelvis, the obturator externus may then take over that task.
As well as flexing the hip, the hip flexors can be used in concert with the hip extensors to stabilize the hip and to help keep the hip joint centered.
To strengthen the hip flexors check out Hip Flexor Strengthening Exercises.
As a yoga teacher, I'm constantly exploring new exercises, new ways of doing yoga poses.
There is no single "right way" of doing a yoga pose. Instead, there are options. And the better you are at "feeling" your body, the better you can get at choosing the right option for your body as it is now.
For any technique, the point of practice is to learn feel it and to control it, so that it can be used without thinking about how to use it.
And that is more or less the approach taken in all of my ebooks and videos. They help you to feel your body and control it so that you can work towards using it effectively in anything that you do.