Grid-forming (GFM) inverters are increasingly deployed in modern power systems due to their strong voltage and frequency support capabilities, as well as their high robustness in weak grids. However, unlike traditional synchronous generators with high overcurrent tolerance, GFM inverters can only withstand 1 to 1.5 per-unit of their rated current due to the thermal limitations of semiconductor switches. Furthermore, current IEEE standards and grid codes require GFM inverters to remain connected to power grids during grid faults, making current limiting the most critical fault ride-through (FRT) capability for ensuring power system safety, stability, and resilience. In addition to current limiting, various IEEE standards and grid codes define additional FRT requirements based on voltage, current, and power. However, a comprehensive summary of the corresponding FRT capabilities required to satisfy these standards remains lacking in existing literature. Therefore, this thesis systematically summarizes voltage ride-through, current ride-through, and power ride-through capabilities of GFM inverters and assigns each FRT capability a priority level using a star-rating system based on its impacts on system safety, stability and resilience. Moreover, based on the priority level, this thesis investigates the challenges associated with achieving current limiting, voltage limiting, voltage support, and active power support in GFM inverters. To address these challenges, this thesis proposes four distinct FRT strategies. First, to achieve the most critical FRT capability of current limiting while ensuring rapid post-fault voltage recovery and maintaining high power quality, this thesis introduces a model-predictive dual-control loop (MPDCL). This strategy also mitigates wind-up issues and eliminates the need for non-trivial weighting factor design. Second, to achieve the secondary critical FRT capability of voltage limiting for specific grounded-ungrounded transformer configurations under single-line-to-ground faults, this thesis proposes a simultaneous overvoltage and overcurrent mitigation strategy. Additionally, it mitigates overcurrent issues, and the mechanism of concurrent overvoltage and overcurrent issues is deduced. Third, to achieve the third critical FRT capability of voltage support in GFM inverters during asymmetrical grid faults, this thesis introduces an adaptive virtual impedance. Besides, the mechanism of enhancing voltage support capability in GFM inverters during asymmetrical grid faults is derived and validated. The voltage support capability is inherently linked to reactive power support, which is typically required by system operators. In contrast to enhancing the reactive power support capability, system operators also expect GFM inverters to provide active power support in certain scenarios. However, enhancing this capability remains underdeveloped, particularly under asymmetrical grid faults. Finally, to increase active power output during asymmetrical grid faults, this thesis presents an active power enhancement control strategy and analyzes the reason of active power curtailment. Ultimately, a set of quantification metrics is developed to evaluate FRT performance across the identified FRT capabilities. These metrics provide an intuitive framework for comparing the advantages and limitations of different FRT strategies and enable real-time system performance assessment. Theoretical analyses and experimental validations further demonstrate the effectiveness of the proposed strategies and metrics, contributing to improved resilience and compliance of GFM inverters with evolving grid codes.