Entanglement islands arise from nontrivial saddle points in the semi-classical path integral computation of the entropy of Hawking radiation via the replica method. Their contribution to the entropy as a function of time yields results that are consistent with the black hole evaporation process being unitary. In this chapter, we discuss a brief derivation of Hawking radiation from the perspective of correlation functions, a description of entropy paradoxes in the eternal black hole, and details of the associated entanglement island computations in two-dimensional models.