1. INTRODUCTION
1.1. The goal and outline of this survey
1.2. Related work not covered by this survey
1.3. A brief review of sum of squares proofs of non-negativity

2. ENHANCING SCALABILITY BY EXPLOITING STRUCTURE
2.1. Exploiting sparsity
2.2. Exploiting symmetry
2.3. Facial reduction

3. ENHANCING SCALABILITY BY PRODUCING LOW-RANK SOLUTIONS

4. SCALABILITY VIA ADMM AND AUGMENTED LAGRANGIAN METHODS

5. TRADING OFF SCALABILITY WITH CONSERVATISM

6. SOFTWARE: SOLVERS AND MODELING LANGUAGES

7. CONCLUSIONS