Fairly and efficiently dividing a set of indivisible objects between a set of agents is a complex problem with a lot of practical applications. These applications range from allocating courses to students to scheduling observation requests on a constellation of Earth observing satellites. In this talk, after a short general introduction on fair division, we will present a very simple yet remarkable allocation protocol: picking sequences. In spite of its simplicity, making it an appealing protocol for practical use, it has nevertheless very interesting theoretical properties. During the presentation, we will particularly focus on the problem of computing an optimal picking sequence and on aspects related to the agents strategic behaviour.