Wakes produced by underwater vehicles, particularly submarines, in density-stratified fluids play a pivotal role across military, academic, and engineering domains. In comparison to homogeneous fluid environments, wakes in stratified flows exhibit distinctive phenomena, including upstream blocking, pancake eddies, internal waves, and variations in hydrodynamic performance. These phenomena are crucial for optimizing the operation of underwater vehicles. This review critically assesses the hydrodynamic and thermodynamic aspects of these wakes through an integration of theoretical, experimental, and numerical approaches. The hydrodynamic wake evolution, comprising near-wake, non-equilibrium, and quasi-two-dimensional regimes, is scrutinized. The underlying physics, encompassing energy transformation, vertical motion suppression, and momentum dissipation, are analyzed in detail. Special emphasis is placed on numerical methods, encompassing diverse approaches and turbulence models and highlighting their differences in fidelity and computational cost. Numerical simulations not only provide insights into the intricate interplay among various factors but also emerge as a crucial focal point for future research directions. In the realm of thermodynamic wakes, we delve into the thermal wake induced by the discharge of high-temperature cooling water and the cold wake resulting from the stirring of seawater. The generation, evolution, and ascent to the free surface of these wakes are explored. Additionally, this review identifies and analyzes current research shortcomings in each aspect. By systematically addressing existing knowledge gaps, our study contributes novel insights that propel academic progress and bear significant implications for submarine engineering. This work not only enhances our understanding of the intricate dynamics involved but also provides a foundation for future research endeavors in this critical field.