The term "Alien" has a variety of definitions and connotations, but the most popular and relevant one refers to extraterrestrial life forms (literally "beyond Earth" life forms, which live on other planets). There are many different speculations on just what aliens might look like and how they might behave, but as yet, no aliens have been discovered anywhere in our solar system, nor on extrasolar planets. Given the sheer number of galaxies, stars, planets, asteroids, moons, etc. in this universe, however, the existence of alien life is regarded by many as all-but undeniable, and Earth contains innumerable proofs that life can thrive in a variety of conditions, which increases the likelihood of alien life. exobiology is speculative but is accepted as a scientific discipline.
Carbon and other chemicals
We like to assume that, like life on Earth, alien life is carbon-based, needs water to survive, and uses DNA and RNA to store and pass on their genes. As such, efforts to locate alien life focus on these characteristics. However, aliens may use a different element in their genetics, such as nitrogen, phosphorus, silicon, or other such elements. (Indeed, a species of bacterium exists on Earth that is carbon-based, but utilizes arsenic in its DNA in place of phosphorus; whether these organisms are aliens or simply an extremely exotic form of terrestrial life, however, remains to be seen.) They may also use a form of genetic material that is wholly different from RNA or DNA, though exactly what such methods would entail is unclear. If these criteria also allow for life, it's altogether possible that life, in one form or another, exists everywhere that chemicals exist.
As alien life has yet to be discovered, religion does little to address them. However, many theorists speculate that depictions of angels, supernatural beings, and polytheistic gods/goddesses even God himself could, in fact, be garbled accounts of alien visitations. If aliens were to be discovered in the modern era, however, the consequences for organized religion would be potentially disastrous, as it would call into question many assertions made in religious stories, such as that humans are God's favored creations.