The China Fusion Engineering Test Reactor (CFETR) and the Huazhong Field Reversed Configuration (HFRC), currently both under intensive physical and engineering designs in China, are the two major projects representative of the lowdensity steady-state and high-density pulsed pathways to fusion. One of the primary tasks of the physics designs for both CFETR and HFRC is the assessment and analysis of the magnetohydrodynamic (MHD) stability of the proposed design schemes. Comprehensive efforts on the assessment of MHD stability of CFETR and HFRC baseline scenarios have led to preliminary progresses that may further benefit engineering designs. For CFETR, the ECCD power and current for full stabilization on NTM have been predicted in this work, as well as the corresponding controlled magnetic island width. A thorough investigation on RWM stability for CFETR is performed. For 80% of the steady state operation scenarios, active control methods may be required for RWM stabilization. The process of disruption mitigation with massive neon injection on CFETR is simulated. The time scale of and consequences of plasma disruption on CFETR are estimated, which are found equivalent to ITER. Major MHD instabilities such as NTM and RWM remain challenge to steady state tokamak operation. On this basis, next steps on CFETR MHD study are planned on NTM, RWM, and SPI disruption mitigation. For HFRC, plasma heating due to 2D adiabatic compression has been demonstrated in NIMROD simulations. The tilt and rotational instabilities grow on ideal MHD time scale in single fluid MHD model as shown from NIMROD calculations. Two-fluid MHD calculations using NIMROD find FLR stabilizing effects on both tilt and rotational modes. Energetic-particle stabilization of tilt mode was previously demonstrated in C-2 experiments and NIMROD simulations. With stabilization on major MHD instabilities from two-fluid and energetic particle effects, FRC may promise to be an alternative route to compact magnetic fusion ignition. To explore such a potential, we plan on further perform analyses of the MHD instabilities in HFRC during magnetic compression process.