Natural theology (or natural religion) is theology based on reason and ordinary experience. Thus it is distinguished from revealed theology (or revealed religion) which is based on scripture and religious experiences of various kinds; and also from transcendental theology, theology from a priori reasoning (see Immanuel Kant et alia).
Thomas Aquinas is the most famous classical proponent of this approach. A later form of natural theology known as deism rejected scripture and prophecy altogether.
Also William Paley described the teleological argument for God. Contemporary criticisms of Paley's work are found in David Hume's posthumous Dialogues Concerning Natural Religion.
Natural theology was originally part of (philosophy and) theology, and theologians still study it; but most of its content also forms part of the philosophy of religion.