High-voltage direct current (HVDC) has received considerable attention due to several advantageous features such as minimum transmission losses, enhanced stability, and control operation. An appropriate model of HVDC is necessary to assess the operating conditions as well as to analyze the transient and steady-state stabilities integrated with the AC networks. Nevertheless, the construction of an HVDC model is challenging due to the high computational cost, which needs huge ranges of modeling experience. Therefore, advanced dynamic modeling of HVDC is necessary to improve stability with minimum power loss. This paper presents a comprehensive review of the various dynamic modeling of the HVDC transmission system. In line with this matter, an in-depth investigation of various HVDC mathematical models is carried out including average-value modeling (AVM), voltage source converter (VSC), and line-commutated converter (LCC). Moreover, numerous stability assessment models of HVDC are outlined with regard to stability improvement models, current-source system stability, HVDC link stability, and steady-state rotor angle stability. In addition, the various control schemes of LCC-HVDC systems and modular multilevel converter- multi-terminal direct current (MMC-MTDC) are highlighted. This paper also identifies the key issues, the problems of the existing HVDC models as well as providing some selective suggestions for future improvement. All the highlighted insights in this review will hopefully lead to increased efforts toward the enhancement of the modeling for the HVDC system.