Theistic evolution, one form of Old Earth Creationism, has been defined in more than one way:
- Theistic evolution (or "evolutionary creation") is the view that evolution occurred, but was planned and guided by God.
- The belief that God planned and created the universe in such a way that life would come into being without any further supernatural intervention
Sometimes it is not a specific theory of how life originally came into being, or how new species of life arose, but is merely:
In most forms, it asserts that life evolved from a common ancestor created by God, who then steered evolution indirectly as a process of creation, and later gave souls to the first humans to raise them above the animals. Proponents of theistic evolution often emphasize the overall message of Genesis and assert that the details of the story are not meant to be taken literally.
Theistic evolutionists reject special creation of nature and its inhabitants and mankind as declared in Genesis chapters one and two and agree that humans and apes shared a common primatical ancestor. The position has come under attack from a variety of sources - Young Earth Creationists raise all of their standard objections to evolution as well as various theological and exegetical problems. Meanwhile, various agnostics and atheists have accused proponents of theistic evolution of not going far enough or of tacking on various ideas for their own emotional comfort and not for any evidence-based reasoning.
In October 1996, Pope John Paul II referred in an address to the Pontifical Academy of Science to "theories of evolution" that could be "more than a hypothesis" which led many to conclude that evolution and Catholicism are compatible. However, the Magisterial Teaching Authority of the Church as explained by several Papal Encyclicals, most notably Humani Generis (promulgated by the Church in 1950) fall short of accepting any form of evolutionism in official Church teaching. The Roman Catholic Church officially teaches that God created all things ex nihilo (out of nothing) by His Word. No Catholic Christian can be compelled or required to accept evolutionism as a component of official Catholic Teaching. In spite of this, many liberal theologians have advanced a heretical form of theistic evolutionism known as Modernism, which was condemned by the Church in several Papal Encyclicals, most notably Pascendi Dominici Gregis  promulgated by Pope St. Pius X in 1907. This remains the official standpoint of the Catholic Church.
Director of the National Institutes of Health, Francis Collins, a former atheist and now an evangelical Christian, founded The Biologos Foundation to promote theistic evolution, as well as "the harmony between science and biblical faith".
William Jennings Bryan wrote that "Theistic evolution may be defined as an anesthetic which deadens the patient’s pain while atheism removes his religion.” Marvin Olasky essentially concurred with this in a recent column chronicling the loss of Christianity from universities/colleges started by churches. 
The outstanding 19th century theologian Charles Hodge asked the question "What is Darwinism?" His answer: "Atheism".  His work has met a deafening silence as a century and a half later his challenge is still not answered.
Francis Collins and theistic evolution
|“||All Christians, creationists included, can find much to like in The Language of God. Collins’ personal story is fascinating. His intention in writing the book is excellent: to spread the word that faith is reasonable. Like Collins, we want to see an end to the widespread false impression that faith and science are incompatible. However, we must sadly conclude that most of Collins’ arguments—his means to the laudable ends that we all want to further—are going down the wrong path. Instead of creating a harmony between faith and science, theistic evolution subsumes the authority of Scripture to the authority of the latest scientific paper, leaving philosophical confusion in its wake.||”|
Jay Richards and his intelligent design colleagues thoroughly dismantled Francis Collins scientific evidence for Darwinism (supposed junk DNA), discredited by recent advances in understanding the genome.  Collins himself has renounced this also. 
Theistic evolution and Intelligent Design
Although theistic evolution and intelligent design (ID) are superficially similar, ID design proponents have made clear that the two are not the same thing. William Dembski has gone so far as to say that, "as far as design theorists are concerned, theistic evolution is American evangelicalism's ill-conceived accommodation to Darwinism."
The primary difference between the two is the perceived role of proof. While most theistic evolutionists are content to accept God on faith alone, intelligent design proponents seek to prove the necessary existence of a designer in the creation of life by scientific means. Watch their recent "The Problem with Theistic Evolution."
Theistic evolution and Progressive Creationism
Theistic evolution is not the same as Progressive Creationism, as the latter rejects evolution and posits a series of distinct creation events.
Theistic evolution and Gap Theory
Theistic evolution is clearly distinct from Gap theory, which robustly rejects any concept of evolutionary thought.
Criticisms of Theistic Evolution
Theistic evolution has been criticized from a larger variety of directions, including Young Earth Creationists, Old Earth Creationists, atheists and agnostics. Young Earth Creationists and some Old Earth Creationists generally consider Theistic Evolution to be heretical or at best, contrary to Biblical teachings. However, many Young Earth Creationists agree that correct knowledge of how they believe God created humanity and such is not a necessary condition for salvation. A notable proponent of theistic evolution is biologist Ken Miller. Proponents of theistic evolution have been accused of subtly undermining science piece by piece.
- American Scientific Affiliation, the largest organization of scientists who are Christians and who believe evolution to be true.
- Reconciling Creation and Science, by an evangelical Protestant Christian identified only as India (her first name)
- http://www.asa3.org/ASA/education/origins/te-guided.htm#top2 "another old-earth view, evolutionary creation (also called theistic evolution), natural evolution was God's method of creation, with the universe designed so physical structures (galaxies, stars, planets) and complex biological organisms (bacteria, fish, dinosaurs, humans) would naturally evolve."
- When, subsequently, some Catholic writers, in spite of this solemn definition of Catholic doctrine, by which such divine authority is claimed for the "entire books with all their parts" as to secure freedom from any error whatsoever, ventured to restrict the truth of Sacred Scripture solely to matters of faith and morals, and to regard other matters, whether in the domain of physical science or history, as "obiter dicta" and - as they contended - in no wise connected with faith, Our Predecessor of immortal memory, Leo XIII in the Encyclical Letter Providentissimus Deus, published on November 18 in the year 1893, justly and rightly condemned these errors and safe-guarded the studies of the Divine Books by most wise precepts and rules.
- (25 April 2017) in Paul Copan, Tremper Longman III, Christopher I. Reese, Michael G. Strauss: Dictionary of Christianity and Science: The Definitive Reference for the Intersection of Christian Faith and Contemporary Science (in English). Zondervan. ISBN 9780310496069.
- "Soaping the slippery slope: Two books document the decline of once-Christian colleges into bastions of unbelief", World Magazine, August 25, 2012, (accessed 08/31/2017)
- Charles Hodge, What Is Darwinism?, Scribner, Armstrand, & Company, New York, 1874. (online)
- God and Evolution: The Problem with Theistic Evolution (accessed 08/31/2017)
- Marvin Olasky, "Admission of Function", World Magazine, July 9,2016.(accessed 08/31/2017)
- What every theologian should know about creation, evolution, and design Center for Interdisciplinary Studies Transactions 3(2), William Demsbki
- The Problem with Theistic Evolution (crossway.org/TheisticEvolution)
- "belief in the historicity of Genesis is not essential to our salvation." Duane Gish Is it possible to be a Christian and an evolutionist? http://www.answersingenesis.org/creation/v11/i4/christian.asp