The Turing degrees measure the computability-theoretic complexity of sets of natural numbers. By coding, they can be used to measure the complexity of other mathematical objects, such as points on the real plane. However, they are often insufficient in effective mathematics. For example, not all continuous functions on the unit interval have Turing degree. In this and other cases, the enumeration degrees—a natural extension of the Turing degrees—turn out to be sufficient. In fact, the degrees of continuous functions give us a proper subclass of the enumeration degrees: the continuous degrees. A larger subclass, the cototal degrees, arises naturally in symbolic dynamics and computable structure theory. We survey recent results about these two subclasses of the enumeration degrees.