Cross-flow heat exchangers are widely used in thermal and energy systems for their compactness and structural simplicity; however, their thermal–hydraulic performance remains strongly constrained by geometric configuration, flow regime, and pressure-drop penalties. This review systematically examines more than four decades of research on cross-flow and compact heat exchangers, covering theoretical, numerical, and experimental investigations. The effects of geometric modifications—such as fin and tube shape, pitch, orientation, and surface interruption—are critically analyzed, revealing that non-uniform, flow-disturbing geometries can enhance heat transfer by 15–50%, albeit often at the cost of increased hydraulic resistance. Studies of mechanical vibration and flow oscillation demonstrate notable enhancements in heat transfer in low-Reynolds-number and buoyancy-dominated regimes when vibration parameters are optimally tuned. The integration of porous media, including metal foams and packed spheres, has shown substantial performance gains, often exceeding 40–90%, though significant pressure-drop challenges accompany this approach. More recently, artificial intelligence and data-driven optimization techniques have emerged as powerful tools for balancing thermal enhancement and hydraulic penalties. Despite these advances, key gaps persist in condensation-dominated applications, low-Reynolds-number regimes, long-term reliability, and experimentally validated coupled thermal–hydraulic optimization. This review consolidates existing knowledge, identifies unresolved challenges, and outlines future research directions towards high-efficiency, application-specific cross-flow heat exchanger design.