Named after its founder, Iyengar Yoga is taught with an emphasis on alignment and to develop the strength and flexibility required to keep the body's muscular/skeletal system in balance. The value of alignment in balancing and protecting the joints, muscles, etc, is very important. Detailed anatomical instructions help guide the student through a safe and effective practice. The student develops a self-awareness through precision of movement. Correct practice of the yoga postures (asanas) will identify problem areas and help bring the body into balance by strengthening and stretching all the major muscle groups. Due to its precision and emphasis on alignment, Iyengar yoga is particularly useful as a tool for physical therapy and rehabilitation.
Iyengar yoga is a physically challenging approach and can be quite strenuous. While there are arguably more vigorous styles, the Iyengar approach is to work towards increasingly more difficult postures and hold them longer; this builds endurance and stamina, and allows the student to get "deeper" into the pose. This also provides time for the neurological mechanisms that allow the muscles to release and extend and have a lasting effect on the connective tissues being stretched.
A typical Iyengar class will usually focus on a group of asanas; the teacher will have a clear purpose in mind and sequence the poses to accomplish that purpose. The plan may be to work on "standing poses" that day, or maybe "seated twists," or backbends, or forward bends, or arm balances, or inversions, etc. Each class is different. Unlike classes in most other styles of yoga (in which you may do a little of everything), Iyengar classes are tyically planned out to concentrate on an area of the body, or particular actions and movements of the body. The asanas for that class will be carefully chosen and sequenced by the teacher to allow the student to more fully and deeply experience and explore the body. This also facilitates the possibility of touching on slightly more challenging and/or advanced poses towards the end of the class. Attempting advanced asanas otherwise would be difficult and can lead to injuries without careful preparation and guidance.
Unique to Iyengar classes is the use of props: straps, blankets, blocks, chairs, and wall ropes may be used to inform and enable one to practice the asanas while maintaining proper body alignment. With the help of props, one can practice an asana correctly and safely, notwithstanding that the final pose may be inaccessible to the student. Students having particular difficulties with a certain asana may be given an alternative pose by the teacher, and often props will be incorporated. Thus, even the inflexible, elderly, or infirm can receive the benefits of the asanas. The value of props has been recognized by the rest of the yoga community in the last few decades so that now yoga blocks and straps have become ubiquitous.
"Inversions" tend to be taught more in Iyengar classes than in most other styles of yoga. Inversions such as shoulder stand, hand stand, fore-arm stand, and head stand are commonly taught, especially in intermediate and advanced level classes. In the Iyengar method, shoulder stands are performed with blankets under the shoulders to help protect the neck. Since students in beginner classes often do not have sufficient upper body strength and flexibility for inversions, the teacher would have them practice asanas that prepare the body for inversions.
To describe some of the other styles, I will quote from an article by Anne Cushman in the 1995 Yoga Journal entitled "The ABC's of Yoga."
Ashtanga & Power Yoga
The Ashtanga (a.k.a. Astanga) yoga popularized by K. Pattabhi Jois (which is not to be confused with the ashtanga yoga codified by Patanjali in the second century) is a fiery, athletic system aimed at purifying, stretching, and strengthening the body by building up tapas, or heat, through vigorous sequences of postures linked by Sun Salutations. The system is based on four increasingly challenging series of asanas, which were purportedly developed hundreds of years ago; Jois says he rediscovered the series in a Calcutta library, recorded in Sanskrit on a crumbling leaf manuscript. After an initial chant, you'll be led non-stop through one of the classic series, which can last from 90 minutes to several hours. There's no time for subtle adjustments or precise instructions - instead, you're encouraged to maintain focus on your breath as you flow from pose to pose. Even the entry-level series contains many fairly advanced postures. Be prepared to sweat (in fact, the heat is generally turned on in the studio to increase the purificatory intensity). Power yoga is based on the ashtanga system and is often loosely used to refer to a vigorous workout.
Developed by Yogi Amrit Desai, this soft, introspective approach often uses prolonged holding of postures to explore and release emotional and spiritual blockages. In a Kripalu class, goal-oriented striving is actively discouraged; precise alignment is less important than a gentle, loving attitude toward one's body and psyche. You'll be continually reminded to pay attention to your mental and emotional states.
This form of hatha yoga concentrates on awakening the subtle energy that lies dormant at the base of the spine and drawing it upward through each of the seven chakras. In addition to postures, a typical class includes chanting, meditation, and lots of traditional breathing exercises (pranayama), such as alternate nostril breathing and the classic "breath of fire." Many kundalini yoga teachers are followers of the Sikh guru Yogi Bhajan, so some classes may have a devotional tone.
Known as "yoga teacher to the stars" in Los Angeles, Bikram Choudhury has devised a standard sequence of 26 postures - repeated in every class - that shape, stretch, and tone the entire body. The heat is turned up in the studio to simulate the climate in India - and to create a sauna-like purifying effect.
In order to choose the style that is right for you, it is helpful to try different classes and different teachers within the styles.