Abstract: Recurrence of a random walk is characterized by the so-called Pólya number which denotes the probability that the particle returns to the origin at least once during the whole time evolution. We extend the concept of recurrence from classical random walks to quantum walks. First, we show that recurrence of a quantum walk is influenced by the additional degrees of freedom offered by quantum mechanics. Second, we discuss the effect of bias on the recurrence properties of a quantum walk. Finally, we illustrate on a simple example that stationary solutions and full revivals are possible in quantum walks.