Kriyā (in Sanskrit "action, deed, effort") most commonly refers to a "completed action", technique or practice within a yoga discipline meant to achieve a specific result. Another meaning of Kriya is an outward physical manifestation of awakened kundalini, such as a spontaneous body movement related to Kundalini energy flow. O Kriya Shakti is "a power of thought" said to be greatly studied by yogis.
Offering inhaling breath into the outgoing breath, and offering the outgoing breath into the inhaling breath, the yogi neutralizes both these breaths; he thus releases the life force from the heart and brings it under his control.
In the ancient text on yoga called the Yoga Sutras of Patanjali, Patanjali gives a description of Kriya Yoga in the second chapter. Yogananda wrote that Patanjali refers to the Kriya technique when he wrote in the Yoga Sutras II:49: Liberation can be attained by that pranayama which is accomplished by disjoining the course of inspiration and expiration.
Kriya Yoga is a simple, psychological method by which human blood is decarbonated and recharged with oxygen. The atoms of this extra oxygen are transmuted into life current to rejuvenate the brain and spinal centers. By stopping the accumulation of venous blood, the yogi is able to lessen or prevent the decay of tissues. The advanced yogi transmutes his cells into energy.
The story of Lahiri Mahasaya receiving initiation into Kriya Yoga by the yogi Mahavatar Babaji in 1861 is recounted in Autobiography of a Yogi. Yogananda wrote that at that meeting, Mahavatar Babaji told Lahiri Mahasaya, "The Kriya Yoga that I am giving to the world through you in this nineteenth century, is a revival of the same science that Krishna gave millenniums ago to Arjuna; and was later known to Patanjali, and to Christ, St. John, St. Paul, and other disciples". Yogananda also wrote that Babaji and Christ were in continual communion and together, "have planned the spiritual technique of salvation for this age."
Yogananda was asked by Mahavatar Babaji to bring Kriya Yoga to the West. Through Lahiri Mahasaya to his disciple, Yukteswar to Yogananda, a disciple of Yukteswar Giri, Yogananda then brought Kriya Yoga to the United States and Europe beginning in 1920 and continues to this day through his organization Self-Realization Fellowship. In India the fellowship is called Yogoda Satsanga Society of India.
The 'Sudarshan Kriya' is actually another famous pseudo scientifc technique in popular culture, that is spun off as a 'novel' idea by its proponents, which actually is the simple phenomenon of 'Respiratory Alkalosis'.  
Sudarshan Kriya includes a number of techniques.
- A slow breath (2–4 breaths per minute) with increased airway resistance, intensifying the sensation of breath in the throat.
- A rapid and forceful breath at 30 breaths per minute (a form of hyperventilation).
- A chant of “om,” three times, with very slow out-breath.
- A rhythmic, cyclical breathing with slow, medium, and fast cycles.
According to the Times of India, Sudarshan Kriya works on mental, physical and spiritual levels.
Every emotion has breathing patterns; for example, if one gets angry then one's breath is short and fast. Similarly, breathing has an impact on the mind (for example, a deep, long breath relaxes the mind.) Through breathing in different patterns, one can influence emotions and gain control over one's mind. Research suggested that it helps in improving well being (improving immunity and detoxification), and peace of mind (reduce stress, enhance brain function). Sudarshan Kriya is taught in various Art of Living courses.
Kriya Yoga by Baba Haidakhan
Publications on Babaji describe Kriya Yoga as practiced by Baba Haidakhan who died in 1984. Haidakhan Babaji, simply called "Babaji" or Bhole Baba by his students and devotees, was a teacher who appeared in northern India (Uttarakhand) and taught publicly from 1970 to 1984.
Some modern teachers and institutions consider the entire Yoga Sutras to be Kriya Yoga, although Patanjali only relates the term Kriya Yoga to these three foundation practices (tap, swadhyay, Ishwar sharnagati). Often, breathing practices with attention along the spine are included, along with other physical practices. It is useful for the student of Yoga to be aware of these different approaches, so as to not get confused by the various public offerings.
Kriya Yoga by Patanjali
Kriya Yoga is described by its practitioners as the ancient Yoga system described in the ancient text on Yoga by Patanjali, also known as the Yoga Sutras of Patanjali. The second chapter of this ancient text begins with a description of this yoga. Although the Yoga Sutras have become the most important text of Yoga, the opinion of most scholars is that Patañjali was not the creator of Yoga, which existed well before him, but merely a great expounder. Various authorities attribute the compilation of the sutras to Patañjali, who is also referenced as the author of a major treatise on Sanskrit grammar, the Mahabhasya. Patañjali was not the first to write about Yoga, other authors had written before him, and he used their writings in his work. However his text became the authority on the subject.
- Helena Petrona Blavatsky (1893 - 1897), The Secret Doctrine, London Theosophical Pub. House, 1893-97, ISBN 0-900588-74-8
- Paramahansa Yogananda (1995). God Talks with Arjuna: The Bhagavad Gita (Verse IV:29), First Edition. Self-Realization Fellowship. ISBN 0-87612-030-3.
- Patanjali (2003). The Yoga-Sutra of Patanjali: A New Translation with Commentary. Shambhala Classics. Translated by Chip Hartranft. ISBN 1-59030-023-8.
- Yogananda, Paramahansa (1997). Autobiography of a Yogi. Self-Realization Fellowship. p. 275, The Science of Kriya Yoga. ISBN 0876120869.
- Yogananda, Paramahansa (1997). Autobiography of a Yogi. Self-Realization Fellowship. p. 273, The Science of Kriya Yoga. ISBN 0876120869.
- Autobiography of a Yogi, chapter 34, Materializing a Palace in the Himalayas, by Paramahansa Yogananda
- Miller, Timothy (1995). America's Alternative Religions. SUNY Press. p. 178. ISBN 0791423972.
- Autobiography of a Yogi, chapter 33, pg.307, by Paramahansa Yogananda
- Autobiography of a Yogi, ch. 26.
- Sudarshan kriya yoga: Breathing for health Sameer A. Zope et al.
- Devi, Gaura (2001). Fire of Transformation. My life with Babaji. Devon, UK: Nymet Press. ISBN 0-9541839-0-8.
- Mishra, Giridhari Lal (2011). From Age to Age: Stories of Haidakhan Babaji. American Haidakhan Samaj. ISBN 978-0578085463.
- Govindan, Marshall (2000). Kriya Yoga Sutras of Patanjali and the Siddhas. Kriya Yoga Publications. ISBN 1-89538-312-9.
- Tola, Fernando; Dragonetti, Carmen; Prithipaul, K. Dad (1987). "Introduction". The Yogasūtras of Patañjali on concentration of mind. Motilal Banarsidass. p. xi.
- The Yoga Sutras of Patanjali, ed. James Haughton Woods, 1914, p. xv
- Kriya Yoga organizations