This paper provides a comprehensive review of the existing research on the Dual Active Bridge (DAB) DC-DC converter, focusing on modeling methods, modulation strategies, optimization algorithms, and control methods. A comparative analysis of selected methods along with guidelines to assist engineers and researchers in their study of DAB is also presented. Firstly, a comprehensive review of modulation strategies for DAB is provided, ranging from classical phase-shift modulation to the popular asymmetric duty modulation. The intrinsic relationships among different modulation methods are summarized, and a comparison is made based on the difficulty of control and DAB operating characteristics. Secondly, the various modeling methods for DAB are described, including reduced-order modeling, generalized state-space averaging modeling, and discrete-time modeling methods. A comparison is made based on the suitability for different application scenarios, providing recommendations for the adoption of different modeling methods. Furthermore, a survey of optimization algorithms for modulation methods is presented, including classical algorithms, swarm intelligence optimization, and reinforcement learning algorithms. A number of criteria are proposed for different algorithms, and an analysis of the unresolved challenges and future prospects is provided. Finally, the advanced control methods for DAB are summarized based on control effectiveness and applicability. The article concludes with a summary and an outlook on future research directions is also provided.