The field of semidefinite programming (SDP) has received considerable attention in the last decade due to its numerous applications and nice theoretical properties. Although interior-point methods can theoretically solve SDPs in polynomial-time and have proven practically effective on small- to medium-scale problems, their practicality on large-scale problems is currently limited due to high computational requirements. In this talk, we will detail recent efforts to solve large-scale SDPs using traditional nonlinear programming (NLP) approaches instead of interior-point methods. In particular, we will show how both the primal and dual SDP can be reformulated to allow the use of fast first-order NLP algorithms such as the limited memory BFGS approach, and we will also provide computational evidence demonstrating the considerable progress that these methods have made on large-scale SDPs.