In radiotherapy for cancer, the total planned dose is usually broken into several equal-dose treatment sessions called fractions that are administered over several weeks. A key challenge here is to choose an optimal number of fractions and the corresponding dosing schedule. This is called the optimal fractionation problem. In this talk, we discuss how to address such a problem by using the linear-quadratic model of dose-response. We introduce both stylized and full-scale optimization models for this problem. Assuming that a fluence-map optimization problem has been solved a priori, we show that a closed-form solution to the optimal fractionation problem can be obtained. Our full-scale model attempts to simultaneously optimize the fluence-map and the number of fractions, resulting in a non-convex problem with many variables and constraints. We present an efficient convex optimization algorithm to approximate the solution of the non-convex problem. Numerical experiments and sensitivity analyses on head-and-neck and prostate cancer test cases will be discussed. Robust and stochastic variations of the fractionation problem may also be discussed if time permits.