The electric rail transport sector is the largest consumer of energy, especially urban railway transit systems. Therefore, there is a need to implement effective solutions to savings and reduce their consumption. Most energy optimization strategies focus on the efficient management of regenerative electric braking energy recovery and storage in storage systems. On-board hybrid energy storage systems, combining multiple technologies, efficiently recycle regenerative braking energy. They mitigate issues like voltage spikes, temperature rise, and energy loss from braking resistors. They also tackle the drawbacks of single-technology systems, which have trouble juggling the demands of power density and energy for urban rail vehicles. This paper first describes energy storage technologies and on-board hybrid energy storage systems in urban railway vehicles. Then, the optimal energy management strategies for urban on-board hybrid energy storage systems are presented, classified into three main categories. The traits, benefits, and drawbacks of every strategy are examined and compiled. The paper's conclusions provide a general overview and potential directions, laying the groundwork for future research into on-board hybrid energy storage systems for urban rail transportation.