The rapid proliferation of data driven decision systems has intensified the demand for rigorous privacy guarantees that do not unduly compromise statistical utility. Differential privacy has emerged as the gold standard for quantifying privacy risk, offering mathematically provable protections against adversarial inference. At the same time, stochastic convex optimization forms the algorithmic backbone of modern machine learning and statistical estimation. The intersection of these two domains has given rise to a rich theoretical literature exploring optimal error rates, algorithmic constructions, geometric tradeoffs, and refined privacy notions such as concentrated and Renyi differential privacy. This article develops a unified and comprehensive theoretical account of private stochastic convex optimization, grounded strictly in foundational and contemporary works on differential privacy, local privacy, private empirical risk minimization, optimal mechanisms, metric geometry of privacy utility tradeoffs, and Langevin based stochastic processes. The paper synthesizes contributions from classical noise calibration and distributed noise generation to modern advances in concentrated and Renyi privacy, and further connects them to minimax optimality under local constraints and to geometric interpretations via Wasserstein metrics and Sobolev norms. We analyze how optimal rates for private empirical risk minimization are achieved, why certain noise distributions such as Laplace mechanisms are optimal under specific constraints, and how Langevin dynamics provide a natural probabilistic interpretation of privacy preserving optimization. We also examine the role of random walks and private measures in synthetic data generation, as well as the implications of mechanism design and distributed noise for economic and multi agent environments. The results demonstrate that optimal private stochastic convex optimization is fundamentally shaped by geometric and probabilistic structures that govern both information leakage and statistical efficiency. By providing an integrative perspective across privacy definitions, algorithmic constructions, and geometric insights, this work identifies deep structural principles underlying privacy utility tradeoffs and outlines future research directions for scalable, theoretically optimal, and practically robust private learning systems.