Voltage source converter high voltage direct current (VSC-HVDC) technology has become increasingly cost-effective and technically feasible in recent years. It is likely to play a vital role in integrating remotely-located renewable generation and reinforcing existing power systems. Multi-terminal VSC-HVDC (MTDC) systems, with superior reliability, redundancy and flexibility over the conventional point-to-point HVDC, have attracted a great deal of attention globally. MTDC however remains an area where little standardisation has taken place, and a series of challenges need to be fully understood and tackled before moving towards more complex DC grids. This thesis investigates modelling, control and stability of MTDC systems. DC voltage, which indicates power balance and stability of DC systems, is of paramount importance in MTDC control. Further investigation is required to understand the dynamic and steady-state behaviours of various DC voltage and active power control schemes in previous literature. This work provides a detailed comparative study of modelling and control methodologies of MTDC systems, with a key focus on the control of grid side converters and DC voltage coordination. A generalised algorithm is proposed to enable MTDC power flow calculations when complex DC voltage control characteristics are employed. Analysis based upon linearised power flow equations and equivalent circuit of droop control is performed to provide further intuitive understanding of the steady-state behaviours of MTDC systems. Information of key constraints on the stability and robustness of MTDC control systems has been limited. A main focus of this thesis is to examine these potential stability limitations and to increase the understanding of MTDC dynamics. In order to perform comprehensive open-loop and closed-loop stability studies, a systematic procedure is developed for mathematical modelling of MTDC systems. The resulting analytical models and frequency domain tools are employed in this thesis to assess the stability, dynamic performance and robustness of active power and DC voltage control of VSC-HVDC. Limitations imposed by weak AC systems, DC system parameters, converter operating point, controller structure, and controller bandwidth on the closed-loop MTDC stability are identified and investigated in detail. Large DC reactors, which are required by DC breaker systems, are identified in this research to have detrimental effects on the controllability, stability and robustness of MTDC voltage control. This could impose a serious challenge for existing control designs. A DC voltage damping controller is proposed to cope with the transient performance issues caused by the DC reactors. Furthermore, two active stabilising controllers are developed to enhance the controllability and robust stability of DC voltage control in a DC grid.