The nonresonant single-phase dual-active-bridge (NSDAB) dc-dc converter has been increasingly adopted for isolated dc-dc power conversion systems. Over the past few years, significant research has been carried out to address the technical challenges associated with modulations and controls of the NSDAB dc-dc converter. The aim of this paper is to review and compare these recent state-of-the-art modulation and control strategies. First, the modulation strategies for the NSDAB dc-dc converter are analyzed. All possible phase-shift patterns are demonstrated, and the correlation analysis of the typical phases-shift modulation methods for the NSDAB dc-dc converter is presented. Then, an overview of steady-state efficiency-optimization strategies is discussed for the NSDAB dc-dc converter. Moreover, a review of optimized techniques for dynamic responses is also provided. For both the efficiency and dynamic optimizations, thorough comparisons and recommendations are provided in this paper. Finally, to improve both steady-state and transient performances, a combination approach to optimize both the efficiency and dynamics for an NSDAB dc-dc converter based on the reviewed methods is presented in this paper.