Large-scale optimization, sometimes called "inverse design" or "topology optimization," involves the computational design of new structures that maximize performance of a device, with so many parameters (hundreds, thousands, or more) that the computer is free to "discover" entirely new geometries rather than simply tweaking a few parameters of a human design. Many authors have applied this approach to an increasing number of problems in photonics over the past 20 years. However, effective use of large-scale optimization in photonics is not simply a matter of blindly throwing more and more parameters at the computer, which often becomes intractable. Nor is it a matter of devising new optimization algorithms — almost all authors use "off the shelf" algorithms. The key, rather, is choosing the right formulation of a given problem, expressing it in such a way as to exploit the best forward solvers and optimization techniques. In this talk, I will present several case studies to illustrate the kinds of ideas that have proven effective: adjoint methods to rapidly evaluate gradients, reformulations of eigenproblems to avoid tricky problems arising from lack of differentiability, continuous relaxations of discrete parameters, and more exotic optics-specific transformations such as deformations of finite-bandwidth problems into the complex frequency plane. Applications include solar cells, nonlinear resonances, photonic bandgap maximization, and optimal plasmonic absorption.