HVDC technology is developing fast and HVDC grids are increasingly seen as a possible and feasible solution to manage the future power system with large amounts of renewables in a secure and cost-effective manner. However, systems with significant amounts of DC transmission behave in a fundamentally different manner when compared to the traditional AC power system. The integration of HVDC systems introduces new fast dynamics on different time frames and adds controllability to the combined system. As a result, the modeling and control of the entire interconnected system needs to be reevaluated in order to accurately compute the system behavior, both from the AC and DC system. This survey paper gives an overview of the current research in the field of HVDC grids focusing on the interaction of the AC and DC system. The converters and their behavior are discussed in greater detail. A second component which is discussed is the DC breaker. Both devices operate fundamentally different than their AC counterparts. The fast interaction between AC and DC systems requires changes in the manner in which the modeling and computation of the system is done, both at the DC and the AC side. Although these considerations are needed within all relevant time frames, two relevant cases are specifically addressed in this paper: the connection of offshore wind power through a HVDC system and the optimal operation of the power system with a strong presence of HVDC.