This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution settings. The survey presents a unified mathematical framework and reviews key application domains including crop selection, production planning, optimal power flow, unit commitment, hydropower scheduling, and energy market operations. General-purpose solvers and domain-specific software tools are examined with respect to their algorithmic foundations and practical limitations. Recent advances in learning-assisted optimization are also reviewed, highlighting how machine learning and reinforcement learning enhance classical solvers through warm-starting, constraint screening, branching strategies, policy approximation, and scenario generation. The paper provides a consolidated reference for scalable and reliable optimization methods in complex agriculture and energy systems.