Knot homology theories associate to a knot or link a complex of graded modules whose graded Euler characteristic is a classical knot polynomial. This type of knot invariant has been increasingly influential in low-dimensional topology in the ten years or so since the first one was developed. This (primarily expository) talk will introduce some knot homology theories with an emphasis on their formal algebraic structures and give examples of their applications. No significant background in low-dimensional topology will be assumed.