This dissertation addresses fundamental challenges in structural biology through the development and application of constraint satisfaction formulations, which are effectively solved using iterative projection methods such as Reflect-Reflect-Relax (RRR). We demonstrate how the divide-and-concur framework, when combined with these methods, can successfully tackle complex structural problems that require the satisfaction of multiple constraints involving molecular geometry, X-ray contrast (electron charge density), and energy models. We begin with a proof-of-concept study involving simplified two-dimensional lattice proteins, composed of only two residues, H (hydrophobic) and P (polar), designed to capture the essential features of globular protein folding. This study establishes the viability of constraint-based approaches for structural prediction problems, demonstrating their effectiveness in solving such systems. Building upon this foundation, we utilize the divide-and-concur framework to address the real protein folding challenge. While protein folding involves complex thermodynamic processes that require a delicate balance of multiple physical forces, our constraint-based approach effectively approximates traditional force field models while offering significant computational advantages. The key innovation lies in incorporating interpretable constraints through the divide-and-concur framework, which systematically reduces the conformational search space. This enhancement enables ab initio folding of miniproteins on standard commercial computers within minutes, representing a substantial improvement in computational efficiency. The versatility of constraint-based methods extends beyond protein folding to other critical structural biology applications, particularly in multi-conformer refinement problems where configuration tangling phenomena arise. The modular nature of the divide-and-concur framework facilitates seamless integration of density constraints, making it particularly well-suited for multi-constraint optimization problems. This work establishes constraint-based approaches as powerful tools for tackling some of the most computationally demanding problems in modern structural biology.