I will present an exciting new interaction between computer science and fair division theory, with the goal of giving the audience a taste of different fair division challenges and the role computational thinking plays in addressing them. Among other things, I will talk about a complexity-theoretic approach to the question of why envy-free cake cutting has been so elusive; and will explain how the notion of worst-case approximation gives rise to a provably feasible notion of fairness in the context of the allocation of indivisible goods. I will also talk about the integration of some of these theoretical ideas into Spliddit (http://www.spliddit.org), a not-for-profit fair division website that aims to make the world just a bit fairer.